code: def dtw_barycenter_averaging_petitjean(
      X,
      barycenter_size=None,
      init_barycenter=None,
      max_iter=30,
      tol=1e-5,
      weights=None,
      metric_params=None,
      verbose=False,
  ):
      """DTW Barycenter Averaging (DBA) method.
  
      DBA was originally presented in [1]_.
      This implementation is not the one documented in the API, but is kept
      in the codebase to check the documented one for non-regression.
  
      Parameters
      ----------
      X : array-like, shape=(n_ts, sz, d)
          Time series dataset.
  
      barycenter_size : int or None (default: None)
          Size of the barycenter to generate. If None, the size of the barycenter
          is that of the data provided at fit
          time or that of the initial barycenter if specified.
  
      init_barycenter : array or None (default: None)
          Initial barycenter to start from for the optimization process.
  
      max_iter : int (default: 30)
          Number of iterations of the Expectation-Maximization optimization
          procedure.
  
      tol : float (default: 1e-5)
          Tolerance to use for early stopping: if the decrease in cost is lower
          than this value, the
          Expectation-Maximization procedure stops.
  
      weights: None or array
          Weights of each X[i]. Must be the same size as len(X).
          If None, uniform weights are used.
  
      metric_params: dict or None (default: None)
          DTW constraint parameters to be used.
          See :ref:`tslearn.metrics.dtw_path <fun-tslearn.metrics.dtw_path>` for
          a list of accepted parameters
          If None, no constraint is used for DTW computations.
  
      verbose : boolean (default: False)
          Whether to print information about the cost at each iteration or not.
  
      Returns
      -------
      numpy.array of shape (barycenter_size, d) or (sz, d) if barycenter_size \
              is None
          DBA barycenter of the provided time series dataset.
  
      Examples
      --------
      >>> time_series = [[1, 2, 3, 4], [1, 2, 4, 5]]
      >>> dtw_barycenter_averaging_petitjean(time_series, max_iter=5)
      array([[1. ],
             [2. ],
             [3.5],
             [4.5]])
      >>> time_series = [[1, 2, 3, 4], [1, 2, 3, 4, 5]]
      >>> dtw_barycenter_averaging_petitjean(time_series, max_iter=5)
      array([[1. ],
             [2. ],
             [3. ],
             [4. ],
             [4.5]])
      >>> dtw_barycenter_averaging_petitjean(time_series, max_iter=5,
      ...                          metric_params={"itakura_max_slope": 2})
      array([[1. ],
             [2. ],
             [3. ],
             [3.5],
             [4.5]])
      >>> dtw_barycenter_averaging_petitjean(time_series, max_iter=5,
      ...                                    barycenter_size=3)
      array([[1.5       ],
             [3.        ],
             [4.33333333]])
      >>> dtw_barycenter_averaging_petitjean([[0, 0, 0], [10, 10, 10]],
      ...                                    weights=numpy.array([0.75, 0.25]))
      array([[2.5],
             [2.5],
             [2.5]])
  
      References
      ----------
      .. [1] F. Petitjean, A. Ketterlin & P. Gancarski. A global averaging method
         for dynamic time warping, with applications to clustering. Pattern
         Recognition, Elsevier, 2011, Vol. 44, Num. 3, pp. 678-693
      """
      X_ = to_time_series_dataset(X)
      if barycenter_size is None:
          barycenter_size = X_.shape[1]
      weights = _set_weights(weights, X_.shape[0])
      if init_barycenter is None:
          barycenter = _init_avg(X_, barycenter_size)
      else:
          barycenter_size = init_barycenter.shape[0]
          barycenter = init_barycenter
      cost_prev, cost = numpy.inf, numpy.inf
      for it in range(max_iter):
          assign = _petitjean_assignment(X_, barycenter, metric_params)
          cost = _petitjean_cost(X_, barycenter, assign, weights)
          if verbose:
              print("[DBA] epoch %d, cost: %.3f" % (it + 1, cost))
          barycenter = _petitjean_update_barycenter(
              X_, assign, barycenter_size, weights
          )
          if abs(cost_prev - cost) < tol:
              break
          elif cost_prev < cost:
              warnings.warn(
                  "DBA loss is increasing while it should not be. "
                  "Stopping optimization.",
                  ConvergenceWarning,
              )
              break
          else:
              cost_prev = cost
      return barycenter
  
imports: import numpy
  import warnings
  from scipy.interpolate import interp1d
  from sklearn.exceptions import ConvergenceWarning
  from sklearn.utils import check_random_state
  from ..metrics import dtw_path
  from ..utils import to_time_series_dataset, ts_size
  from .utils import _set_weights
label_desc: Use image node_id 5 for calling a global function with example usage: dtw_barycenter_averaging_petitjean(X, barycenter_size, init_barycenter, max_iter, tol, weights, metric_params, verbose) and returns: barycenter