code: from __future__ import annotations
  from typing import Tuple, NoReturn
  
  import IMLearn.metrics
  from ...base import BaseEstimator
  import numpy as np
  from itertools import product
  
  
  class DecisionStump(BaseEstimator):
      """
      A decision stump classifier for {-1,1} labels according to the CART algorithm
  
      Attributes
      ----------
      self.threshold_ : float
          The threshold by which the data is split
  
      self.j_ : int
          The index of the feature by which to split the data
  
      self.sign_: int
          The label to predict for samples where the value of the j'th
           feature is about the threshold
      """
  
      def __init__(self) -> DecisionStump:
          """
          Instantiate a Decision stump classifier
          """
          super().__init__()
          self.threshold_, self.j_, self.sign_ = None, None, None
  
      def _fit(self, X: np.ndarray, y: np.ndarray) -> NoReturn:
          """
          fits a decision stump to the given data
  
          Parameters
          ----------
          X : ndarray of shape (n_samples, n_features)
              Input data to fit an estimator for
  
          y : ndarray of shape (n_samples, )
              Responses of input data to fit to
          """
          err = np.inf
          for j in range(len(X[0])):
              feature = X[:, j]
              for sign in (-1, 1):
                  thr, tre_err = self._find_threshold(feature, y, sign)
                  if tre_err < err:
                      err, self.j_, self.threshold_, self.sign_ = tre_err, j, \
                                                                  thr, sign
  
      def _predict(self, X: np.ndarray) -> np.ndarray:
          """
          Predict responses for given samples using fitted estimator
  
          Parameters
          ----------
          X : ndarray of shape (n_samples, n_features)
              Input data to predict responses for
  
          Returns
          -------
          responses : ndarray of shape (n_samples, )
              Predicted responses of given samples
  
          Notes
          -----
          Feature values strictly below threshold are predicted as `-sign`
           whereas values which equal
          to or above the threshold are predicted as `sign`
          """
          return np.where(X[:, self.j_] < self.threshold_, self.sign_ * -1,
                          self.sign_)
  
      def _find_threshold(self, values: np.ndarray, labels: np.ndarray,
                          sign: int) -> Tuple[float, float]:
          """
          Given a feature vector and labels, find a threshold by which to perform a split
          The threshold is found according to the value minimizing the misclassification
          error along this feature
  
          Parameters
          ----------
          values: ndarray of shape (n_samples,)
              A feature vector to find a splitting threshold for
  
          labels: ndarray of shape (n_samples,)
              The labels to compare against
  
          sign: int
              Predicted label assigned to values equal to or above threshold
  
          Returns
          -------
          thr: float
              Threshold by which to perform split
  
          thr_err: float between 0 and 1
              Misclassificaiton error of returned threshold
  
          Notes
          -----
          For every tested threshold, values strictly below threshold are
          predicted as `-sign` whereas values
          which equal to or above the threshold are predicted as `sign`
          """
          cut, err = 0, 1
          sort_label = labels[np.argsort(values)]
          sort_feature = np.sort(values)
          n_samples = values.shape[0]
          ones = np.ones(n_samples) * sign
          for i in range(n_samples):
              n_e = np.sum(
                  np.where(np.sign(ones) != np.sign(sort_label),
                           np.abs(sort_label), 0)) / \
                    n_samples
              if n_e < err:
                  cut, err = sort_feature[i], n_e
              ones[i] *= -1  # update the threshold placement.
  
          return cut, err
  
  
      def _loss(self, X: np.ndarray, y: np.ndarray) -> float:
          """
          Evaluate performance under misclassification loss function
  
          Parameters
          ----------
          X : ndarray of shape (n_samples, n_features)
              Test samples
  
          y : ndarray of shape (n_samples, )
              True labels of test samples
  
          Returns
          -------
          loss : float
              Performance under missclassification loss function
          """
          from ...metrics.loss_functions import misclassification_error
          return misclassification_error(y, self.predict(X))
  
apis: numpy.ones numpy.sign numpy.argsort numpy.abs numpy.sort numpy.where