code: def dict_learning_online(
      X,
      n_components=2,
      *,
      alpha=1,
      n_iter="deprecated",
      max_iter=None,
      return_code=True,
      dict_init=None,
      callback=None,
      batch_size=256,
      verbose=False,
      shuffle=True,
      n_jobs=None,
      method="lars",
      iter_offset="deprecated",
      random_state=None,
      return_inner_stats="deprecated",
      inner_stats="deprecated",
      return_n_iter="deprecated",
      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.
  
      n_iter : int, default=100
          Number of mini-batch iterations to perform.
  
          .. deprecated:: 1.1
             `n_iter` is deprecated in 1.1 and will be removed in 1.4. Use
             `max_iter` instead.
  
      max_iter : int, default=None
          Maximum number of iterations over the complete dataset before
          stopping independently of any early stopping criterion heuristics.
          If ``max_iter`` is not None, ``n_iter`` is ignored.
  
          .. versionadded:: 1.1
  
      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.
  
      iter_offset : int, default=0
          Number of previous iterations completed on the dictionary used for
          initialization.
  
          .. deprecated:: 1.1
             `iter_offset` serves internal purpose only and will be removed in 1.4.
  
      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>`.
  
      return_inner_stats : bool, default=False
          Return the inner statistics A (dictionary covariance) and B
          (data approximation). Useful to restart the algorithm in an
          online setting. If `return_inner_stats` is `True`, `return_code` is
          ignored.
  
          .. deprecated:: 1.1
             `return_inner_stats` serves internal purpose only and will be removed in 1.4.
  
      inner_stats : tuple of (A, B) ndarrays, default=None
          Inner sufficient statistics that are kept by the algorithm.
          Passing them at initialization is useful in online settings, to
          avoid losing the history of the evolution.
          `A` `(n_components, n_components)` is the dictionary covariance matrix.
          `B` `(n_features, n_components)` is the data approximation matrix.
  
          .. deprecated:: 1.1
             `inner_stats` serves internal purpose only and will be removed in 1.4.
  
      return_n_iter : bool, default=False
          Whether or not to return the number of iterations.
  
          .. deprecated:: 1.1
             `return_n_iter` will be removed in 1.4 and n_iter will never be returned.
  
      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. Used only if `max_iter` is not None.
  
          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. Used only if
          `max_iter` is not None.
  
          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.
      """
      deps = (
          return_n_iter,
          return_inner_stats,
          iter_offset,
          inner_stats,
      )
      if max_iter is not None and not all(
          arg == "deprecated" for arg in deps
      ):
          raise ValueError(
              "The following arguments are incompatible with 'max_iter': "
              "return_n_iter, return_inner_stats, iter_offset, inner_stats"
          )
  
      iter_offset = _check_warn_deprecated(
          iter_offset, "iter_offset", default=0
      )
      return_inner_stats = _check_warn_deprecated(
          return_inner_stats,
          "return_inner_stats",
          default=False,
          additional_message="From 1.4 inner_stats will never be returned.",
      )
      inner_stats = _check_warn_deprecated(
          inner_stats, "inner_stats", default=None
      )
      return_n_iter = _check_warn_deprecated(
          return_n_iter,
          "return_n_iter",
          default=False,
          additional_message=(
              "From 1.4 'n_iter' will never be returned. Refer to the 'n_iter_' and "
              "'n_steps_' attributes of the MiniBatchDictionaryLearning object instead."
          ),
      )
  
      if max_iter is not None:
          transform_algorithm = "lasso_" + method
  
          est = MiniBatchDictionaryLearning(
              n_components=n_components,
              alpha=alpha,
              n_iter=n_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_
  
      # TODO(1.4) remove the whole old behavior
      # Fallback to old behavior
  
      n_iter = _check_warn_deprecated(
          n_iter,
          "n_iter",
          default=100,
          additional_message="Use 'max_iter' instead.",
      )
  
      if n_components is None:
          n_components = X.shape[1]
  
      if method not in ("lars", "cd"):
          raise ValueError(
              "Coding method not supported as a fit algorithm."
          )
  
      _check_positive_coding(method, positive_code)
  
      method = "lasso_" + method
  
      t0 = time.time()
      n_samples, n_features = X.shape
      # Avoid integer division problems
      alpha = float(alpha)
      random_state = check_random_state(random_state)
  
      # Init V with SVD of X
      if dict_init is not None:
          dictionary = dict_init
      else:
          _, S, dictionary = randomized_svd(
              X, n_components, random_state=random_state
          )
          dictionary = S[:, np.newaxis] * dictionary
      r = len(dictionary)
      if n_components <= r:
          dictionary = dictionary[:n_components, :]
      else:
          dictionary = np.r_[
              dictionary,
              np.zeros(
                  (n_components - r, dictionary.shape[1]),
                  dtype=dictionary.dtype,
              ),
          ]
  
      if verbose == 1:
          print("[dict_learning]", end=" ")
  
      if shuffle:
          X_train = X.copy()
          random_state.shuffle(X_train)
      else:
          X_train = X
  
      X_train = check_array(
          X_train, order="C", dtype=[np.float64, np.float32], copy=False
      )
  
      # Fortran-order dict better suited for the sparse coding which is the
      # bottleneck of this algorithm.
      dictionary = check_array(
          dictionary, order="F", dtype=X_train.dtype, copy=False
      )
      dictionary = np.require(dictionary, requirements="W")
  
      batches = gen_batches(n_samples, batch_size)
      batches = itertools.cycle(batches)
  
      # The covariance of the dictionary
      if inner_stats is None:
          A = np.zeros(
              (n_components, n_components), dtype=X_train.dtype
          )
          # The data approximation
          B = np.zeros((n_features, n_components), dtype=X_train.dtype)
      else:
          A = inner_stats[0].copy()
          B = inner_stats[1].copy()
  
      # If n_iter is zero, we need to return zero.
      ii = iter_offset - 1
  
      for ii, batch in zip(
          range(iter_offset, iter_offset + n_iter), batches
      ):
          this_X = X_train[batch]
          dt = time.time() - t0
          if verbose == 1:
              sys.stdout.write(".")
              sys.stdout.flush()
          elif verbose:
              if verbose > 10 or ii % ceil(100.0 / verbose) == 0:
                  print(
                      "Iteration % 3i (elapsed time: % 3is, % 4.1fmn)"
                      % (ii, dt, dt / 60)
                  )
  
          this_code = sparse_encode(
              this_X,
              dictionary,
              algorithm=method,
              alpha=alpha,
              n_jobs=n_jobs,
              check_input=False,
              positive=positive_code,
              max_iter=method_max_iter,
              verbose=verbose,
          )
  
          # Update the auxiliary variables
          if ii < batch_size - 1:
              theta = float((ii + 1) * batch_size)
          else:
              theta = float(batch_size**2 + ii + 1 - batch_size)
          beta = (theta + 1 - batch_size) / (theta + 1)
  
          A *= beta
          A += np.dot(this_code.T, this_code)
          B *= beta
          B += np.dot(this_X.T, this_code)
  
          # Update dictionary in place
          _update_dict(
              dictionary,
              this_X,
              this_code,
              A,
              B,
              verbose=verbose,
              random_state=random_state,
              positive=positive_dict,
          )
  
          # Maybe we need a stopping criteria based on the amount of
          # modification in the dictionary
          if callback is not None:
              callback(locals())
  
      if return_inner_stats:
          if return_n_iter:
              return dictionary, (A, B), ii - iter_offset + 1
          else:
              return dictionary, (A, B)
      if return_code:
          if verbose > 1:
              print("Learning code...", end=" ")
          elif verbose == 1:
              print("|", end=" ")
          code = sparse_encode(
              X,
              dictionary,
              algorithm=method,
              alpha=alpha,
              n_jobs=n_jobs,
              check_input=False,
              positive=positive_code,
              max_iter=method_max_iter,
              verbose=verbose,
          )
          if verbose > 1:
              dt = time.time() - t0
              print(
                  "done (total time: % 3is, % 4.1fmn)" % (dt, dt / 60)
              )
          if return_n_iter:
              return code, dictionary, ii - iter_offset + 1
          else:
              return code, dictionary
  
      if return_n_iter:
          return dictionary, ii - iter_offset + 1
      else:
          return dictionary
  
imports: import itertools
  import sys
  import time
  import warnings
  from math import ceil
  from numbers import Integral, Real
  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 8 for calling a global function with example usage: dict_learning_online(X, n_components) and returns: dictionary,  unknown, dictionary, est, code,  est, dictionary,  A,  B,  unknown, dictionary,  A,  B, code,  dictionary,  unknown, code,  dictionary