code: def dict_learning_online(
      X,
      n_components=2,
      alpha=1,
      n_iter=100,
      return_code=True,
      dict_init=None,
      callback=None,
      batch_size=3,
      verbose=False,
      shuffle=True,
      n_jobs=1,
      method="lars",
      iter_offset=0,
      random_state=None,
      return_inner_stats=False,
      inner_stats=None,
      return_n_iter=False,
  ):
      """Solves 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 ||_2^2 + alpha * || U ||_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. This is
      accomplished by repeatedly iterating over mini-batches by slicing
      the input data.
  
      Read more in the :ref:`User Guide <DictionaryLearning>`.
  
      Parameters
      ----------
      X: array of shape (n_samples, n_features)
          Data matrix.
  
      n_components : int,
          Number of dictionary atoms to extract.
  
      alpha : float,
          Sparsity controlling parameter.
  
      n_iter : int,
          Number of iterations to perform.
  
      return_code : boolean,
          Whether to also return the code U or just the dictionary V.
  
      dict_init : array of shape (n_components, n_features),
          Initial value for the dictionary for warm restart scenarios.
  
      callback :
          Callable that gets invoked every five iterations.
  
      batch_size : int,
          The number of samples to take in each batch.
  
      verbose :
          Degree of output the procedure will print.
  
      shuffle : boolean,
          Whether to shuffle the data before splitting it in batches.
  
      n_jobs : int,
          Number of parallel jobs to run, or -1 to autodetect.
  
      method : {'lars', 'cd'}
          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.
  
      random_state : int or RandomState
          Pseudo number generator state used for random sampling.
  
      return_inner_stats : boolean, optional
          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
  
      inner_stats : tuple of (A, B) ndarrays
          Inner sufficient statistics that are kept by the algorithm.
          Passing them at initialization is useful in online settings, to
          avoid loosing 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
  
      return_n_iter : bool
          Whether or not to return the number of iterations.
  
      Returns
      -------
      code : array of shape (n_samples, n_components),
          the sparse code (only returned if `return_code=True`)
  
      dictionary : array 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
      DictionaryLearning
      MiniBatchDictionaryLearning
      SparsePCA
      MiniBatchSparsePCA
  
      """
      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."
          )
      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)
  
      if n_jobs == -1:
          n_jobs = cpu_count()
  
      # 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])),
          ]
  
      if verbose == 1:
          print("[dict_learning]", end=" ")
  
      if shuffle:
          X_train = X.copy()
          random_state.shuffle(X_train)
      else:
          X_train = X
  
      dictionary = check_array(
          dictionary.T, order="F", dtype=np.float64, copy=False
      )
      X_train = check_array(
          X_train, order="C", dtype=np.float64, copy=False
      )
  
      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))
          # The data approximation
          B = np.zeros((n_features, n_components))
      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.T,
              algorithm=method,
              alpha=alpha,
              n_jobs=n_jobs,
          ).T
  
          # 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, this_code.T)
          B *= beta
          B += np.dot(this_X.T, this_code.T)
  
          # Update dictionary
          dictionary = _update_dict(
              dictionary,
              B,
              A,
              verbose=verbose,
              random_state=random_state,
          )
          # XXX: Can the residuals be of any use?
  
          # 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.T, (A, B), ii - iter_offset + 1
          else:
              return dictionary.T, (A, B)
      if return_code:
          if verbose > 1:
              print("Learning code...", end=" ")
          elif verbose == 1:
              print("|", end=" ")
          code = sparse_encode(
              X,
              dictionary.T,
              algorithm=method,
              alpha=alpha,
              n_jobs=n_jobs,
              check_input=False,
          )
          if verbose > 1:
              dt = time.time() - t0
              print(
                  "done (total time: % 3is, % 4.1fmn)" % (dt, dt / 60)
              )
          if return_n_iter:
              return code, dictionary.T, ii - iter_offset + 1
          else:
              return code, dictionary.T
  
      if return_n_iter:
          return dictionary.T, ii - iter_offset + 1
      else:
          return dictionary.T
  
imports: from __future__ import print_function
  import time
  import sys
  import itertools
  from math import sqrt, ceil
  import numpy
  from scipy import linalg
  from numpy.lib.stride_tricks import as_strided
  from ..base import BaseEstimator, TransformerMixin
  from ..externals.joblib import Parallel, delayed, cpu_count
  from ..externals.six.moves import zip
  from ..utils import check_array, check_random_state, gen_even_slices, gen_batches, _get_n_jobs
  from ..utils.extmath import randomized_svd, row_norms
  from ..utils.validation import check_is_fitted
  from ..linear_model import Lasso, orthogonal_mp_gram, LassoLars, Lars
label_desc: Use image node_id 5 for calling a global function with example usage: dict_learning_online(X, n_components, alpha, n_iter, return_code, dict_init, callback, batch_size, verbose, shuffle, n_jobs, method, iter_offset, random_state, return_inner_stats, inner_stats, return_n_iter) and returns: dictionary,  unknown, dictionary, dictionary,  A,  B,  unknown, dictionary,  A,  B, code,  dictionary,  unknown, code,  dictionary