code: def make_classification(
      n_samples=100,
      n_features=20,
      *,
      n_informative=2,
      n_redundant=2,
      n_repeated=0,
      n_classes=2,
      n_clusters_per_class=2,
      weights=None,
      flip_y=0.01,
      class_sep=1.0,
      hypercube=True,
      shift=0.0,
      scale=1.0,
      shuffle=True,
      random_state=None,
  ):
      """Generate a random n-class classification problem.
  
      This initially creates clusters of points normally distributed (std=1)
      about vertices of an ``n_informative``-dimensional hypercube with sides of
      length ``2*class_sep`` and assigns an equal number of clusters to each
      class. It introduces interdependence between these features and adds
      various types of further noise to the data.
  
      Without shuffling, ``X`` horizontally stacks features in the following
      order: the primary ``n_informative`` features, followed by ``n_redundant``
      linear combinations of the informative features, followed by ``n_repeated``
      duplicates, drawn randomly with replacement from the informative and
      redundant features. The remaining features are filled with random noise.
      Thus, without shuffling, all useful features are contained in the columns
      ``X[:, :n_informative + n_redundant + n_repeated]``.
  
      Read more in the :ref:`User Guide <sample_generators>`.
  
      Parameters
      ----------
      n_samples : int, default=100
          The number of samples.
  
      n_features : int, default=20
          The total number of features. These comprise ``n_informative``
          informative features, ``n_redundant`` redundant features,
          ``n_repeated`` duplicated features and
          ``n_features-n_informative-n_redundant-n_repeated`` useless features
          drawn at random.
  
      n_informative : int, default=2
          The number of informative features. Each class is composed of a number
          of gaussian clusters each located around the vertices of a hypercube
          in a subspace of dimension ``n_informative``. For each cluster,
          informative features are drawn independently from  N(0, 1) and then
          randomly linearly combined within each cluster in order to add
          covariance. The clusters are then placed on the vertices of the
          hypercube.
  
      n_redundant : int, default=2
          The number of redundant features. These features are generated as
          random linear combinations of the informative features.
  
      n_repeated : int, default=0
          The number of duplicated features, drawn randomly from the informative
          and the redundant features.
  
      n_classes : int, default=2
          The number of classes (or labels) of the classification problem.
  
      n_clusters_per_class : int, default=2
          The number of clusters per class.
  
      weights : array-like of shape (n_classes,) or (n_classes - 1,),\
                default=None
          The proportions of samples assigned to each class. If None, then
          classes are balanced. Note that if ``len(weights) == n_classes - 1``,
          then the last class weight is automatically inferred.
          More than ``n_samples`` samples may be returned if the sum of
          ``weights`` exceeds 1. Note that the actual class proportions will
          not exactly match ``weights`` when ``flip_y`` isn't 0.
  
      flip_y : float, default=0.01
          The fraction of samples whose class is assigned randomly. Larger
          values introduce noise in the labels and make the classification
          task harder. Note that the default setting flip_y > 0 might lead
          to less than ``n_classes`` in y in some cases.
  
      class_sep : float, default=1.0
          The factor multiplying the hypercube size.  Larger values spread
          out the clusters/classes and make the classification task easier.
  
      hypercube : bool, default=True
          If True, the clusters are put on the vertices of a hypercube. If
          False, the clusters are put on the vertices of a random polytope.
  
      shift : float, ndarray of shape (n_features,) or None, default=0.0
          Shift features by the specified value. If None, then features
          are shifted by a random value drawn in [-class_sep, class_sep].
  
      scale : float, ndarray of shape (n_features,) or None, default=1.0
          Multiply features by the specified value. If None, then features
          are scaled by a random value drawn in [1, 100]. Note that scaling
          happens after shifting.
  
      shuffle : bool, default=True
          Shuffle the samples and the features.
  
      random_state : int, RandomState instance or None, default=None
          Determines random number generation for dataset creation. Pass an int
          for reproducible output across multiple function calls.
          See :term:`Glossary <random_state>`.
  
      Returns
      -------
      X : ndarray of shape (n_samples, n_features)
          The generated samples.
  
      y : ndarray of shape (n_samples,)
          The integer labels for class membership of each sample.
  
      See Also
      --------
      make_blobs : Simplified variant.
      make_multilabel_classification : Unrelated generator for multilabel tasks.
  
      Notes
      -----
      The algorithm is adapted from Guyon [1] and was designed to generate
      the "Madelon" dataset.
  
      References
      ----------
      .. [1] I. Guyon, "Design of experiments for the NIPS 2003 variable
             selection benchmark", 2003.
      """
      generator = check_random_state(random_state)
  
      # Count features, clusters and samples
      if n_informative + n_redundant + n_repeated > n_features:
          raise ValueError(
              "Number of informative, redundant and repeated "
              "features must sum to less than the number of total"
              " features"
          )
      # Use log2 to avoid overflow errors
      if n_informative < np.log2(n_classes * n_clusters_per_class):
          msg = "n_classes({}) * n_clusters_per_class({}) must be"
          msg += " smaller or equal 2**n_informative({})={}"
          raise ValueError(
              msg.format(
                  n_classes,
                  n_clusters_per_class,
                  n_informative,
                  2**n_informative,
              )
          )
  
      if weights is not None:
          if len(weights) not in [n_classes, n_classes - 1]:
              raise ValueError(
                  "Weights specified but incompatible with number of classes."
              )
          if len(weights) == n_classes - 1:
              if isinstance(weights, list):
                  weights = weights + [1.0 - sum(weights)]
              else:
                  weights = np.resize(weights, n_classes)
                  weights[-1] = 1.0 - sum(weights[:-1])
      else:
          weights = [1.0 / n_classes] * n_classes
  
      n_useless = n_features - n_informative - n_redundant - n_repeated
      n_clusters = n_classes * n_clusters_per_class
  
      # Distribute samples among clusters by weight
      n_samples_per_cluster = [
          int(n_samples * weights[k % n_classes] / n_clusters_per_class)
          for k in range(n_clusters)
      ]
  
      for i in range(n_samples - sum(n_samples_per_cluster)):
          n_samples_per_cluster[i % n_clusters] += 1
  
      # Initialize X and y
      X = np.zeros((n_samples, n_features))
      y = np.zeros(n_samples, dtype=int)
  
      # Build the polytope whose vertices become cluster centroids
      centroids = _generate_hypercube(
          n_clusters, n_informative, generator
      ).astype(float, copy=False)
      centroids *= 2 * class_sep
      centroids -= class_sep
      if not hypercube:
          centroids *= generator.uniform(size=(n_clusters, 1))
          centroids *= generator.uniform(size=(1, n_informative))
  
      # Initially draw informative features from the standard normal
      X[:, :n_informative] = generator.standard_normal(
          size=(n_samples, n_informative)
      )
  
      # Create each cluster; a variant of make_blobs
      stop = 0
      for k, centroid in enumerate(centroids):
          start, stop = stop, stop + n_samples_per_cluster[k]
          y[start:stop] = k % n_classes  # assign labels
          X_k = X[
              start:stop, :n_informative
          ]  # slice a view of the cluster
  
          A = (
              2 * generator.uniform(size=(n_informative, n_informative))
              - 1
          )
          X_k[...] = np.dot(X_k, A)  # introduce random covariance
  
          X_k += centroid  # shift the cluster to a vertex
  
      # Create redundant features
      if n_redundant > 0:
          B = (
              2 * generator.uniform(size=(n_informative, n_redundant))
              - 1
          )
          X[:, n_informative : n_informative + n_redundant] = np.dot(
              X[:, :n_informative], B
          )
  
      # Repeat some features
      if n_repeated > 0:
          n = n_informative + n_redundant
          indices = (
              (n - 1) * generator.uniform(size=n_repeated) + 0.5
          ).astype(np.intp)
          X[:, n : n + n_repeated] = X[:, indices]
  
      # Fill useless features
      if n_useless > 0:
          X[:, -n_useless:] = generator.standard_normal(
              size=(n_samples, n_useless)
          )
  
      # Randomly replace labels
      if flip_y >= 0.0:
          flip_mask = generator.uniform(size=n_samples) < flip_y
          y[flip_mask] = generator.randint(
              n_classes, size=flip_mask.sum()
          )
  
      # Randomly shift and scale
      if shift is None:
          shift = (
              2 * generator.uniform(size=n_features) - 1
          ) * class_sep
      X += shift
  
      if scale is None:
          scale = 1 + 100 * generator.uniform(size=n_features)
      X *= scale
  
      if shuffle:
          # Randomly permute samples
          X, y = util_shuffle(X, y, random_state=generator)
  
          # Randomly permute features
          indices = np.arange(n_features)
          generator.shuffle(indices)
          X[:, :] = X[:, indices]
  
      return X, y
  
imports: import array
  import numbers
  import warnings
  from collections.abc import Iterable
  from numbers import Integral, Real
  import numpy
  import scipy.sparse
  from scipy import linalg
  from ..preprocessing import MultiLabelBinarizer
  from ..utils import check_array, check_random_state
  from ..utils import shuffle
  from ..utils._param_validation import Hidden, Interval, StrOptions, validate_params
  from ..utils.random import sample_without_replacement
label_desc: Use image node_id 2 for calling a global function with example usage: make_classification(n_samples, n_features) and returns: X,  y