code: def _initialize_components(
      n_components,
      input,
      y=None,
      init="auto",
      verbose=False,
      random_state=None,
      has_classes=True,
  ):
      """Returns the initial transformation to be used depending on the arguments.
  
      Parameters
      ----------
      n_components : int
        The number of components to take. (Note: it should have been checked
        before, meaning it should not be None and it should be a value in
        [1, X.shape[1]])
  
      input : array-like
        The input samples (can be tuples or regular samples).
  
      y : array-like or None
        The input labels (or not if there are no labels).
  
      init : string or numpy array, optional (default='auto')
        Initialization of the linear transformation. Possible options are
        'auto', 'pca', 'lda', 'identity', 'random', and a numpy array of shape
        (n_features_a, n_features_b).
  
        'auto'
          Depending on ``n_components``, the most reasonable initialization
          will be chosen. If ``n_components <= n_classes`` we use 'lda' (see
          the description of 'lda' init), as it uses labels information. If
          not, but ``n_components < min(n_features, n_samples)``, we use 'pca',
          as it projects data onto meaningful directions (those of higher
          variance). Otherwise, we just use 'identity'.
  
        'pca'
          ``n_components`` principal components of the inputs passed
          to :meth:`fit` will be used to initialize the transformation.
          (See `sklearn.decomposition.PCA`)
  
        'lda'
          ``min(n_components, n_classes)`` most discriminative
          components of the inputs passed to :meth:`fit` will be used to
          initialize the transformation. (If ``n_components > n_classes``,
          the rest of the components will be zero.) (See
          `sklearn.discriminant_analysis.LinearDiscriminantAnalysis`).
          This initialization is possible only if `has_classes == True`.
  
        'identity'
          The identity matrix. If ``n_components`` is strictly smaller than the
          dimensionality of the inputs passed to :meth:`fit`, the identity
          matrix will be truncated to the first ``n_components`` rows.
  
        'random'
          The initial transformation will be a random array of shape
          `(n_components, n_features)`. Each value is sampled from the
          standard normal distribution.
  
        numpy array
          n_features_b must match the dimensionality of the inputs passed to
          :meth:`fit` and n_features_a must be less than or equal to that.
          If ``n_components`` is not None, n_features_a must match it.
  
      verbose : bool
        Whether to print the details of the initialization or not.
  
      random_state : int or `numpy.RandomState` or None, optional (default=None)
        A pseudo random number generator object or a seed for it if int. If
        ``init='random'``, ``random_state`` is used to initialize the random
        transformation. If ``init='pca'``, ``random_state`` is passed as an
        argument to PCA when initializing the transformation.
  
      has_classes : bool (default=True)
        Whether the labels are in fact classes. If true, this will allow to use
        the 'lda' initialization.
  
      Returns
      -------
      init_components : `numpy.ndarray`
        The initial transformation to use.
      """
      # if we are doing a regression we cannot use lda:
      n_features = input.shape[-1]
      authorized_inits = ["auto", "pca", "identity", "random"]
      if has_classes:
          authorized_inits.append("lda")
  
      if isinstance(init, np.ndarray):
          # we copy the array, so that if we update the metric, we don't want to
          # update the init
          init = check_array(init, copy=True)
  
          # Assert that init.shape[1] = X.shape[1]
          if init.shape[1] != n_features:
              raise ValueError(
                  "The input dimensionality ({}) of the given "
                  "linear transformation `init` must match the "
                  "dimensionality of the given inputs `X` ({}).".format(
                      init.shape[1], n_features
                  )
              )
  
          # Assert that init.shape[0] <= init.shape[1]
          if init.shape[0] > init.shape[1]:
              raise ValueError(
                  "The output dimensionality ({}) of the given "
                  "linear transformation `init` cannot be "
                  "greater than its input dimensionality ({}).".format(
                      init.shape[0], init.shape[1]
                  )
              )
  
          # Assert that self.n_components = init.shape[0]
          if n_components != init.shape[0]:
              raise ValueError(
                  "The preferred dimensionality of the "
                  "projected space `n_components` ({}) does"
                  " not match the output dimensionality of "
                  "the given linear transformation "
                  "`init` ({})!".format(n_components, init.shape[0])
              )
      elif init not in authorized_inits:
          raise ValueError(
              "`init` must be '{}' "
              "or a numpy array of shape (n_components, n_features).".format(
                  "', '".join(authorized_inits)
              )
          )
  
      random_state = check_random_state(random_state)
      if isinstance(init, np.ndarray):
          return init
      n_samples = input.shape[0]
      if init == "auto":
          if has_classes:
              n_classes = len(np.unique(y))
          else:
              n_classes = -1
          init = _auto_select_init(
              has_classes,
              n_features,
              n_samples,
              n_components,
              n_classes,
          )
      if init == "identity":
          return np.eye(n_components, input.shape[-1])
      elif init == "random":
          return random_state.randn(n_components, input.shape[-1])
      elif init in {"pca", "lda"}:
          init_time = time.time()
          if init == "pca":
              pca = PCA(
                  n_components=n_components, random_state=random_state
              )
              if verbose:
                  print("Finding principal components... ")
                  sys.stdout.flush()
              pca.fit(input)
              transformation = pca.components_
          elif init == "lda":
              lda = LinearDiscriminantAnalysis(
                  n_components=n_components
              )
              if verbose:
                  print("Finding most discriminative components... ")
                  sys.stdout.flush()
              lda.fit(input, y)
              transformation = lda.scalings_.T[:n_components]
          if verbose:
              print("done in {:5.2f}s".format(time.time() - init_time))
          return transformation
  
imports: import numpy
  from numpy.linalg import LinAlgError
  from sklearn.datasets import make_spd_matrix
  from sklearn.decomposition import PCA
  from sklearn.utils import check_array
  from sklearn.utils.validation import check_X_y, check_random_state
  from .exceptions import PreprocessorError, NonPSDError
  from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
  from scipy.linalg import pinvh, eigh
  import sys
  import time
  import warnings
label_desc: Use image node_id 15 for calling a global function with example usage: _initialize_components(n_components, input, y, init, verbose, random_state, has_classes) and returns: init, np, random_state, transformation