code: def fastica(
      X,
      n_components=None,
      algorithm="parallel",
      whiten=True,
      fun="logcosh",
      fun_args=None,
      max_iter=200,
      tol=1e-04,
      w_init=None,
      random_state=None,
      return_X_mean=False,
      compute_sources=True,
      return_n_iter=False,
  ):
      """Perform Fast Independent Component Analysis.
  
      Read more in the :ref:`User Guide <ICA>`.
  
      Parameters
      ----------
      X : array-like, shape (n_samples, n_features)
          Training vector, where n_samples is the number of samples and
          n_features is the number of features.
  
      n_components : int, optional
          Number of components to extract. If None no dimension reduction
          is performed.
  
      algorithm : {'parallel', 'deflation'}, optional
          Apply a parallel or deflational FASTICA algorithm.
  
      whiten : boolean, optional
          If True perform an initial whitening of the data.
          If False, the data is assumed to have already been
          preprocessed: it should be centered, normed and white.
          Otherwise you will get incorrect results.
          In this case the parameter n_components will be ignored.
  
      fun : string or function, optional. Default: 'logcosh'
          The functional form of the G function used in the
          approximation to neg-entropy. Could be either 'logcosh', 'exp',
          or 'cube'.
          You can also provide your own function. It should return a tuple
          containing the value of the function, and of its derivative, in the
          point. Example:
  
          def my_g(x):
              return x ** 3, 3 * x ** 2
  
      fun_args : dictionary, optional
          Arguments to send to the functional form.
          If empty or None and if fun='logcosh', fun_args will take value
          {'alpha' : 1.0}
  
      max_iter : int, optional
          Maximum number of iterations to perform.
  
      tol: float, optional
          A positive scalar giving the tolerance at which the
          un-mixing matrix is considered to have converged.
  
      w_init : (n_components, n_components) array, optional
          Initial un-mixing array of dimension (n.comp,n.comp).
          If None (default) then an array of normal r.v.'s is used.
  
      random_state : int or RandomState
          Pseudo number generator state used for random sampling.
  
      return_X_mean : bool, optional
          If True, X_mean is returned too.
  
      compute_sources : bool, optional
          If False, sources are not computed, but only the rotation matrix.
          This can save memory when working with big data. Defaults to True.
  
      return_n_iter : bool, optional
          Whether or not to return the number of iterations.
  
      Returns
      -------
      K : array, shape (n_components, n_features) | None.
          If whiten is 'True', K is the pre-whitening matrix that projects data
          onto the first n_components principal components. If whiten is 'False',
          K is 'None'.
  
      W : array, shape (n_components, n_components)
          Estimated un-mixing matrix.
          The mixing matrix can be obtained by::
  
              w = np.dot(W, K.T)
              A = w.T * (w * w.T).I
  
      S : array, shape (n_samples, n_components) | None
          Estimated source matrix
  
      X_mean : array, shape (n_features, )
          The mean over features. Returned only if return_X_mean is True.
  
      n_iter : int
          If the algorithm is "deflation", n_iter is the
          maximum number of iterations run across all components. Else
          they are just the number of iterations taken to converge. This is
          returned only when return_n_iter is set to `True`.
  
      Notes
      -----
  
      The data matrix X is considered to be a linear combination of
      non-Gaussian (independent) components i.e. X = AS where columns of S
      contain the independent components and A is a linear mixing
      matrix. In short ICA attempts to `un-mix' the data by estimating an
      un-mixing matrix W where ``S = W K X.``
  
      This implementation was originally made for data of shape
      [n_features, n_samples]. Now the input is transposed
      before the algorithm is applied. This makes it slightly
      faster for Fortran-ordered input.
  
      Implemented using FastICA:
      `A. Hyvarinen and E. Oja, Independent Component Analysis:
      Algorithms and Applications, Neural Networks, 13(4-5), 2000,
      pp. 411-430`
  
      """
      random_state = check_random_state(random_state)
      fun_args = {} if fun_args is None else fun_args
      # make interface compatible with other decompositions
      # a copy is required only for non whitened data
      X = check_array(X, copy=whiten, dtype=FLOAT_DTYPES).T
  
      alpha = fun_args.get("alpha", 1.0)
      if not 1 <= alpha <= 2:
          raise ValueError("alpha must be in [1,2]")
  
      if fun == "logcosh":
          g = _logcosh
      elif fun == "exp":
          g = _exp
      elif fun == "cube":
          g = _cube
      elif callable(fun):
  
          def g(x, fun_args):
              return fun(x, **fun_args)
  
      else:
          exc = (
              ValueError
              if isinstance(fun, six.string_types)
              else TypeError
          )
          raise exc(
              "Unknown function %r;"
              " should be one of 'logcosh', 'exp', 'cube' or callable"
              % fun
          )
  
      n, p = X.shape
  
      if not whiten and n_components is not None:
          n_components = None
          warnings.warn("Ignoring n_components with whiten=False.")
  
      if n_components is None:
          n_components = min(n, p)
      if n_components > min(n, p):
          n_components = min(n, p)
          warnings.warn(
              "n_components is too large: it will be set to %s"
              % n_components
          )
  
      if whiten:
          # Centering the columns (ie the variables)
          X_mean = X.mean(axis=-1)
          X -= X_mean[:, np.newaxis]
  
          # Whitening and preprocessing by PCA
          u, d, _ = linalg.svd(X, full_matrices=False)
  
          del _
          K = (u / d).T[:n_components]  # see (6.33) p.140
          del u, d
          X1 = np.dot(K, X)
          # see (13.6) p.267 Here X1 is white and data
          # in X has been projected onto a subspace by PCA
          X1 *= np.sqrt(p)
      else:
          # X must be casted to floats to avoid typing issues with numpy
          # 2.0 and the line below
          X1 = as_float_array(
              X, copy=False
          )  # copy has been taken care of
  
      if w_init is None:
          w_init = np.asarray(
              random_state.normal(size=(n_components, n_components)),
              dtype=X1.dtype,
          )
  
      else:
          w_init = np.asarray(w_init)
          if w_init.shape != (n_components, n_components):
              raise ValueError(
                  "w_init has invalid shape -- should be %(shape)s"
                  % {"shape": (n_components, n_components)}
              )
  
      kwargs = {
          "tol": tol,
          "g": g,
          "fun_args": fun_args,
          "max_iter": max_iter,
          "w_init": w_init,
      }
  
      if algorithm == "parallel":
          W, n_iter = _ica_par(X1, **kwargs)
      elif algorithm == "deflation":
          W, n_iter = _ica_def(X1, **kwargs)
      else:
          raise ValueError(
              "Invalid algorithm: must be either `parallel` or"
              " `deflation`."
          )
      del X1
  
      if whiten:
          if compute_sources:
              S = fast_dot(fast_dot(W, K), X).T
          else:
              S = None
          if return_X_mean:
              if return_n_iter:
                  return K, W, S, X_mean, n_iter
              else:
                  return K, W, S, X_mean
          else:
              if return_n_iter:
                  return K, W, S, n_iter
              else:
                  return K, W, S
  
      else:
          if compute_sources:
              S = fast_dot(W, X).T
          else:
              S = None
          if return_X_mean:
              if return_n_iter:
                  return None, W, S, None, n_iter
              else:
                  return None, W, S, None
          else:
              if return_n_iter:
                  return None, W, S, n_iter
              else:
                  return None, W, S
  
imports: import warnings
  import numpy
  from scipy import linalg
  from ..base import BaseEstimator, TransformerMixin
  from ..externals import six
  from ..externals.six import moves
  from ..utils import check_array, as_float_array, check_random_state
  from ..utils.extmath import fast_dot
  from ..utils.validation import check_is_fitted
  from ..utils.validation import FLOAT_DTYPES
label_desc: Use image node_id 8 for calling a global function with example usage: fastica(X, n_components, algorithm, whiten, fun, fun_args, max_iter, tol, w_init, random_state, return_X_mean, compute_sources, return_n_iter) and returns: K,  W,  S,  X_mean,  n_iter, K,  W,  S,  X_mean, K,  W,  S,  n_iter, K,  W,  S, None,  W,  S,  None,  n_iter, None,  W,  S,  None, None,  W,  S,  n_iter, None,  W,  S, fun