code: def group_sparse_covariance_path(
      train_subjs,
      alphas,
      test_subjs=None,
      tol=1e-3,
      max_iter=10,
      precisions_init=None,
      verbose=0,
      debug=False,
      probe_function=None,
  ):
      """Get estimated precision matrices for different values of alpha.
  
      Calling this function is faster than calling group_sparse_covariance()
      repeatedly, because it makes use of the first result to initialize the
      next computation.
  
      Parameters
      ----------
      train_subjs : list of numpy.ndarray
          list of signals.
  
      alphas : list of float
           values of alpha to use. Best results for sorted values (decreasing)
  
      test_subjs : list of numpy.ndarray, optional
          list of signals, independent from those in train_subjs, on which to
          compute a score. If None, no score is computed.
  
      verbose : int, default=0
          verbosity level.
  
      tol, max_iter, debug, precisions_init :
          Passed to group_sparse_covariance(). See the corresponding docstring
          for details.
  
      probe_function : callable, 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.
  
      Returns
      -------
      precisions_list : list of numpy.ndarray
          estimated precisions for each value of alpha provided. The length of
          this list is the same as that of parameter "alphas".
  
      scores : list of float
          for each estimated precision, score obtained on the test set. Output
          only if test_subjs is not None.
  
      """
      train_covs, train_n_samples = empirical_covariances(
          train_subjs, assume_centered=False, standardize=True
      )
  
      scores = []
      precisions_list = []
      for alpha in alphas:
          precisions = _group_sparse_covariance(
              train_covs,
              train_n_samples,
              alpha,
              tol=tol,
              max_iter=max_iter,
              precisions_init=precisions_init,
              verbose=max(0, verbose - 1),
              debug=debug,
              probe_function=probe_function,
          )
  
          # Compute log-likelihood
          if test_subjs is not None:
              test_covs, _ = empirical_covariances(
                  test_subjs, assume_centered=False, standardize=True
              )
              scores.append(
                  group_sparse_scores(
                      precisions, train_n_samples, test_covs, 0
                  )[0]
              )
          precisions_list.append(precisions)
          precisions_init = precisions
  
      return (
          (precisions_list, scores)
          if test_subjs is not None
          else precisions_list
      )
  
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 8 for calling a global function with example usage: group_sparse_covariance_path(train_subjs, alphas, test_subjs, tol, max_iter, precisions_init, verbose, debug, probe_function) and returns: unknown