code: def dict_learning_online(
      X,
      n_components=2,
      *,
      alpha=1,
      max_iter=100,
      return_code=True,
      dict_init=None,
      callback=None,
      batch_size=256,
      verbose=False,
      shuffle=True,
      n_jobs=None,
      method="lars",
      random_state=None,
      positive_dict=False,
      positive_code=False,
      method_max_iter=1000,
      tol=1e-3,
      max_no_improvement=10,
  ):
      """Solve a dictionary learning matrix factorization problem online.
  
      Finds the best dictionary and the corresponding sparse code for
      approximating the data matrix X by solving::
  
          (U^*, V^*) = argmin 0.5 || X - U V ||_Fro^2 + alpha * || U ||_1,1
                       (U,V)
                       with || V_k ||_2 = 1 for all  0 <= k < n_components
  
      where V is the dictionary and U is the sparse code. ||.||_Fro stands for
      the Frobenius norm and ||.||_1,1 stands for the entry-wise matrix norm
      which is the sum of the absolute values of all the entries in the matrix.
      This is accomplished by repeatedly iterating over mini-batches by slicing
      the input data.
  
      Read more in the :ref:`User Guide <DictionaryLearning>`.
  
      Parameters
      ----------
      X : ndarray of shape (n_samples, n_features)
          Data matrix.
  
      n_components : int or None, default=2
          Number of dictionary atoms to extract. If None, then ``n_components``
          is set to ``n_features``.
  
      alpha : float, default=1
          Sparsity controlling parameter.
  
      max_iter : int, default=100
          Maximum number of iterations over the complete dataset before
          stopping independently of any early stopping criterion heuristics.
  
          .. versionadded:: 1.1
  
          .. deprecated:: 1.4
             `max_iter=None` is deprecated in 1.4 and will be removed in 1.6.
             Use the default value (i.e. `100`) instead.
  
      return_code : bool, default=True
          Whether to also return the code U or just the dictionary `V`.
  
      dict_init : ndarray of shape (n_components, n_features), default=None
          Initial values for the dictionary for warm restart scenarios.
          If `None`, the initial values for the dictionary are created
          with an SVD decomposition of the data via
          :func:`~sklearn.utils.extmath.randomized_svd`.
  
      callback : callable, default=None
          A callable that gets invoked at the end of each iteration.
  
      batch_size : int, default=256
          The number of samples to take in each batch.
  
          .. versionchanged:: 1.3
             The default value of `batch_size` changed from 3 to 256 in version 1.3.
  
      verbose : bool, default=False
          To control the verbosity of the procedure.
  
      shuffle : bool, default=True
          Whether to shuffle the data before splitting it in batches.
  
      n_jobs : int, default=None
          Number of parallel jobs to run.
          ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
          ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
          for more details.
  
      method : {'lars', 'cd'}, default='lars'
          * `'lars'`: uses the least angle regression method to solve the lasso
            problem (`linear_model.lars_path`);
          * `'cd'`: uses the coordinate descent method to compute the
            Lasso solution (`linear_model.Lasso`). Lars will be faster if
            the estimated components are sparse.
  
      random_state : int, RandomState instance or None, default=None
          Used for initializing the dictionary when ``dict_init`` is not
          specified, randomly shuffling the data when ``shuffle`` is set to
          ``True``, and updating the dictionary. Pass an int for reproducible
          results across multiple function calls.
          See :term:`Glossary <random_state>`.
  
      positive_dict : bool, default=False
          Whether to enforce positivity when finding the dictionary.
  
          .. versionadded:: 0.20
  
      positive_code : bool, default=False
          Whether to enforce positivity when finding the code.
  
          .. versionadded:: 0.20
  
      method_max_iter : int, default=1000
          Maximum number of iterations to perform when solving the lasso problem.
  
          .. versionadded:: 0.22
  
      tol : float, default=1e-3
          Control early stopping based on the norm of the differences in the
          dictionary between 2 steps.
  
          To disable early stopping based on changes in the dictionary, set
          `tol` to 0.0.
  
          .. versionadded:: 1.1
  
      max_no_improvement : int, default=10
          Control early stopping based on the consecutive number of mini batches
          that does not yield an improvement on the smoothed cost function.
  
          To disable convergence detection based on cost function, set
          `max_no_improvement` to None.
  
          .. versionadded:: 1.1
  
      Returns
      -------
      code : ndarray of shape (n_samples, n_components),
          The sparse code (only returned if `return_code=True`).
  
      dictionary : ndarray of shape (n_components, n_features),
          The solutions to the dictionary learning problem.
  
      n_iter : int
          Number of iterations run. Returned only if `return_n_iter` is
          set to `True`.
  
      See Also
      --------
      dict_learning : Solve a dictionary learning matrix factorization problem.
      DictionaryLearning : Find a dictionary that sparsely encodes data.
      MiniBatchDictionaryLearning : A faster, less accurate, version of the dictionary
          learning algorithm.
      SparsePCA : Sparse Principal Components Analysis.
      MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis.
  
      Examples
      --------
      >>> import numpy as np
      >>> from sklearn.datasets import make_sparse_coded_signal
      >>> from sklearn.decomposition import dict_learning_online
      >>> X, _, _ = make_sparse_coded_signal(
      ...     n_samples=30, n_components=15, n_features=20, n_nonzero_coefs=10,
      ...     random_state=42,
      ... )
      >>> U, V = dict_learning_online(
      ...     X, n_components=15, alpha=0.2, max_iter=20, batch_size=3, random_state=42
      ... )
  
      We can check the level of sparsity of `U`:
  
      >>> np.mean(U == 0)
      0.53...
  
      We can compare the average squared euclidean norm of the reconstruction
      error of the sparse coded signal relative to the squared euclidean norm of
      the original signal:
  
      >>> X_hat = U @ V
      >>> np.mean(np.sum((X_hat - X) ** 2, axis=1) / np.sum(X ** 2, axis=1))
      0.05...
      """
      # TODO(1.6): remove in 1.6
      if max_iter is None:
          warn(
              (
                  "`max_iter=None` is deprecated in version 1.4 and will be removed in "
                  "version 1.6. Use the default value (i.e. `100`) instead."
              ),
              FutureWarning,
          )
          max_iter = 100
  
      transform_algorithm = "lasso_" + method
  
      est = MiniBatchDictionaryLearning(
          n_components=n_components,
          alpha=alpha,
          max_iter=max_iter,
          n_jobs=n_jobs,
          fit_algorithm=method,
          batch_size=batch_size,
          shuffle=shuffle,
          dict_init=dict_init,
          random_state=random_state,
          transform_algorithm=transform_algorithm,
          transform_alpha=alpha,
          positive_code=positive_code,
          positive_dict=positive_dict,
          transform_max_iter=method_max_iter,
          verbose=verbose,
          callback=callback,
          tol=tol,
          max_no_improvement=max_no_improvement,
      ).fit(X)
  
      if not return_code:
          return est.components_
      else:
          code = est.transform(X)
          return code, est.components_
  
imports: import itertools
  import sys
  import time
  from numbers import Integral, Real
  from warnings import warn
  import numpy
  from joblib import effective_n_jobs
  from scipy import linalg
  from ..base import BaseEstimator, ClassNamePrefixFeaturesOutMixin, TransformerMixin, _fit_context
  from ..linear_model import Lars, Lasso, LassoLars, orthogonal_mp_gram
  from ..utils import check_array, check_random_state, gen_batches, gen_even_slices
  from ..utils._param_validation import Hidden, Interval, StrOptions, validate_params
  from ..utils.extmath import randomized_svd, row_norms, svd_flip
  from ..utils.parallel import Parallel, delayed
  from ..utils.validation import check_is_fitted
label_desc: Use image node_id 7 for calling a global function with example usage: dict_learning_online(X, n_components) and returns: est, code,  est