code: def graphical_lasso(
      emp_cov,
      alpha,
      *,
      cov_init=None,
      mode="cd",
      tol=1e-4,
      enet_tol=1e-4,
      max_iter=100,
      verbose=False,
      return_costs=False,
      eps=np.finfo(np.float64).eps,
      return_n_iter=False,
  ):
      """L1-penalized covariance estimator.
  
      Read more in the :ref:`User Guide <sparse_inverse_covariance>`.
  
      .. versionchanged:: v0.20
          graph_lasso has been renamed to graphical_lasso
  
      Parameters
      ----------
      emp_cov : array-like of shape (n_features, n_features)
          Empirical covariance from which to compute the covariance estimate.
  
      alpha : float
          The regularization parameter: the higher alpha, the more
          regularization, the sparser the inverse covariance.
          Range is (0, inf].
  
      cov_init : array of shape (n_features, n_features), default=None
          The initial guess for the covariance. If None, then the empirical
          covariance is used.
  
          .. deprecated:: 1.3
             `cov_init` is deprecated in 1.3 and will be removed in 1.5.
             It currently has no effect.
  
      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. Range is (0, inf].
  
      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'. Range is (0, inf].
  
      max_iter : int, default=100
          The maximum number of iterations.
  
      verbose : bool, default=False
          If verbose is True, the objective function and dual gap are
          printed at each iteration.
  
      return_costs : bool, default=False
          If return_costs is True, the objective function and dual gap
          at each iteration are returned.
  
      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`.
  
      return_n_iter : bool, default=False
          Whether or not to return the number of iterations.
  
      Returns
      -------
      covariance : ndarray of shape (n_features, n_features)
          The estimated covariance matrix.
  
      precision : ndarray of shape (n_features, n_features)
          The estimated (sparse) precision matrix.
  
      costs : list of (objective, dual_gap) pairs
          The list of values of the objective function and the dual gap at
          each iteration. Returned only if return_costs is True.
  
      n_iter : int
          Number of iterations. Returned only if `return_n_iter` is set to True.
  
      See Also
      --------
      GraphicalLasso : Sparse inverse covariance estimation
          with an l1-penalized estimator.
      GraphicalLassoCV : Sparse inverse covariance with
          cross-validated choice of the l1 penalty.
  
      Notes
      -----
      The algorithm employed to solve this problem is the GLasso algorithm,
      from the Friedman 2008 Biostatistics paper. It is the same algorithm
      as in the R `glasso` package.
  
      One possible difference with the `glasso` R package is that the
      diagonal coefficients are not penalized.
      """
  
      if cov_init is not None:
          warnings.warn(
              (
                  "The cov_init parameter is deprecated in 1.3 and will be removed in "
                  "1.5. It does not have any effect."
              ),
              FutureWarning,
          )
  
      model = GraphicalLasso(
          alpha=alpha,
          mode=mode,
          covariance="precomputed",
          tol=tol,
          enet_tol=enet_tol,
          max_iter=max_iter,
          verbose=verbose,
          eps=eps,
          assume_centered=True,
      ).fit(emp_cov)
  
      output = [model.covariance_, model.precision_]
      if return_costs:
          output.append(model.costs_)
      if return_n_iter:
          output.append(model.n_iter_)
      return tuple(output)
  
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 5 for calling a global function with example usage: graphical_lasso(emp_cov, alpha) and returns: tuple