code: def dict_learning(
      X,
      n_components,
      alpha,
      max_iter=100,
      tol=1e-8,
      method="lars",
      n_jobs=1,
      dict_init=None,
      code_init=None,
      callback=None,
      verbose=False,
      random_state=None,
      return_n_iter=False,
  ):
      """Solves a dictionary learning matrix factorization problem.
  
      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.
  
      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 : int,
          Sparsity controlling parameter.
  
      max_iter : int,
          Maximum number of iterations to perform.
  
      tol : float,
          Tolerance for the stopping condition.
  
      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.
  
      n_jobs : int,
          Number of parallel jobs to run, or -1 to autodetect.
  
      dict_init : array of shape (n_components, n_features),
          Initial value for the dictionary for warm restart scenarios.
  
      code_init : array of shape (n_samples, n_components),
          Initial value for the sparse code for warm restart scenarios.
  
      callback :
          Callable that gets invoked every five iterations.
  
      verbose :
          Degree of output the procedure will print.
  
      random_state : int or RandomState
          Pseudo number generator state used for random sampling.
  
      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 factor in the matrix factorization.
  
      dictionary : array of shape (n_components, n_features),
          The dictionary factor in the matrix factorization.
  
      errors : array
          Vector of errors at each iteration.
  
      n_iter : int
          Number of iterations run. Returned only if `return_n_iter` is
          set to True.
  
      See also
      --------
      dict_learning_online
      DictionaryLearning
      MiniBatchDictionaryLearning
      SparsePCA
      MiniBatchSparsePCA
      """
      if method not in ("lars", "cd"):
          raise ValueError(
              "Coding method %r not supported as a fit algorithm."
              % method
          )
      method = "lasso_" + method
  
      t0 = time.time()
      # Avoid integer division problems
      alpha = float(alpha)
      random_state = check_random_state(random_state)
  
      if n_jobs == -1:
          n_jobs = cpu_count()
  
      # Init the code and the dictionary with SVD of Y
      if code_init is not None and dict_init is not None:
          code = np.array(code_init, order="F")
          # Don't copy V, it will happen below
          dictionary = dict_init
      else:
          code, S, dictionary = linalg.svd(X, full_matrices=False)
          dictionary = S[:, np.newaxis] * dictionary
      r = len(dictionary)
      if n_components <= r:  # True even if n_components=None
          code = code[:, :n_components]
          dictionary = dictionary[:n_components, :]
      else:
          code = np.c_[code, np.zeros((len(code), n_components - r))]
          dictionary = np.r_[
              dictionary,
              np.zeros((n_components - r, dictionary.shape[1])),
          ]
  
      # Fortran-order dict, as we are going to access its row vectors
      dictionary = np.array(dictionary, order="F")
  
      residuals = 0
  
      errors = []
      current_cost = np.nan
  
      if verbose == 1:
          print("[dict_learning]", end=" ")
  
      # If max_iter is 0, number of iterations returned should be zero
      ii = -1
  
      for ii in range(max_iter):
          dt = time.time() - t0
          if verbose == 1:
              sys.stdout.write(".")
              sys.stdout.flush()
          elif verbose:
              print(
                  "Iteration % 3i "
                  "(elapsed time: % 3is, % 4.1fmn, current cost % 7.3f)"
                  % (ii, dt, dt / 60, current_cost)
              )
  
          # Update code
          code = sparse_encode(
              X,
              dictionary,
              algorithm=method,
              alpha=alpha,
              init=code,
              n_jobs=n_jobs,
          )
          # Update dictionary
          dictionary, residuals = _update_dict(
              dictionary.T,
              X.T,
              code.T,
              verbose=verbose,
              return_r2=True,
              random_state=random_state,
          )
          dictionary = dictionary.T
  
          # Cost function
          current_cost = 0.5 * residuals + alpha * np.sum(np.abs(code))
          errors.append(current_cost)
  
          if ii > 0:
              dE = errors[-2] - errors[-1]
              # assert(dE >= -tol * errors[-1])
              if dE < tol * errors[-1]:
                  if verbose == 1:
                      # A line return
                      print("")
                  elif verbose:
                      print(
                          "--- Convergence reached after %d iterations"
                          % ii
                      )
                  break
          if ii % 5 == 0 and callback is not None:
              callback(locals())
  
      if return_n_iter:
          return code, dictionary, errors, ii + 1
      else:
          return code, dictionary, errors
  
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 4 for calling a global function with example usage: dict_learning(X, n_components, alpha, max_iter, tol, method, n_jobs, dict_init, code_init, callback, verbose, random_state, return_n_iter) and returns: code,  dictionary,  errors,  unknown, code,  dictionary,  errors