code: def group_sparse_covariance(
      subjects,
      alpha,
      max_iter=50,
      tol=1e-3,
      verbose=0,
      probe_function=None,
      precisions_init=None,
      debug=False,
  ):
      """Compute sparse precision matrices and covariance matrices.
  
      The precision matrices returned by this function are sparse, and share a
      common sparsity pattern: all have zeros at the same location. This is
      achieved by simultaneous computation of all precision matrices at the
      same time.
  
      Running time is linear on max_iter, and number of subjects (len(subjects)),
      but cubic on number of features (subjects[0].shape[1]).
  
      The present algorithm is based on :footcite:t:`Honorio2015`.
  
      Parameters
      ----------
      subjects : list of numpy.ndarray
          input subjects. Each subject is a 2D array, whose columns contain
          signals. Each array shape must be (sample number, feature number).
          The sample number can vary from subject to subject, but all subjects
          must have the same number of features (i.e. of columns).
  
      alpha : float
          regularization parameter. With normalized covariances matrices and
          number of samples, sensible values lie in the [0, 1] range(zero is
          no regularization: output is not sparse)
  
      max_iter : int, default=50
          maximum number of iterations.
  
      tol : positive float or None, default=1e-3
          The tolerance to declare convergence: if the duality gap goes below
          this value, optimization is stopped. If None, no check is performed.
  
      verbose : int, default=0
          verbosity level. Zero means "no message".
  
      probe_function : callable or None, optional
          This value is called before the first iteration and after each
          iteration. If it returns True, then optimization is stopped
          prematurely.
          The function is given as arguments (in that order):
  
          - empirical covariances (ndarray),
          - number of samples for each subject (ndarray),
          - regularization parameter (float)
          - maximum iteration number (integer)
          - tolerance (float)
          - current iteration number (integer). -1 means "before first iteration"
          - current value of precisions (ndarray).
          - previous value of precisions (ndarray). None before first iteration.
  
      precisions_init : numpy.ndarray, optional
          initial value of the precision matrices. If not provided, a diagonal
          matrix with the variances of each input signal is used.
  
      debug : bool, default=False
          if True, perform checks during computation. It can help find
          numerical problems, but increases computation time a lot.
  
      Returns
      -------
      emp_covs : numpy.ndarray, shape (n_features, n_features, n_subjects)
          empirical covariances matrices
  
      precisions : numpy.ndarray, shape (n_features, n_features, n_subjects)
          estimated precision matrices
  
      References
      ----------
      .. footbibliography::
  
      """
      emp_covs, n_samples = empirical_covariances(
          subjects, assume_centered=False
      )
  
      precisions = _group_sparse_covariance(
          emp_covs,
          n_samples,
          alpha,
          max_iter=max_iter,
          tol=tol,
          verbose=verbose,
          precisions_init=precisions_init,
          probe_function=probe_function,
          debug=debug,
      )
  
      return emp_covs, precisions
  
imports: import collections.abc
  import itertools
  import operator
  import warnings
  import numpy
  import scipy.linalg
  from joblib import Memory, Parallel, delayed
  from sklearn.base import BaseEstimator
  from sklearn.covariance import empirical_covariance
  from sklearn.model_selection import check_cv
  from sklearn.utils.extmath import fast_logdet
  from .._utils import CacheMixin, logger
  from .._utils.extmath import is_spd
label_desc: Use image node_id 4 for calling a global function with example usage: group_sparse_covariance(subjects, alpha, max_iter, tol, verbose, probe_function, precisions_init, debug) and returns: emp_covs,  precisions