text: from __future__ import annotations
  from typing import Tuple, NoReturn
  from ...base import BaseEstimator
  import numpy as np
  from ...metrics import weighted_misclassification_error
  from itertools import product
  
  EPSILON = 1.0
  
  
  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
          """
          n_features = X.shape[1]
          x_tran = X.transpose()
          err = np.zeros((n_features, 2))
          thr = np.zeros((n_features, 2))
          for f in range(len(x_tran)):
              thr[f, 0], err[f, 0] = self._find_threshold(x_tran[f], y, -1)
              thr[f, 1], err[f, 1] = self._find_threshold(x_tran[f], y, 1)
          self.j_, self.sign_ = np.unravel_index(np.argmin(err, axis=None), err.shape)
          self.threshold_ = thr[self.j_][self.sign_]
          self.sign_ = -1 + 2* self.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
  
          y : ndarray of shape (n_samples, )
              Responses of input data to fit to
  
          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`
          """
          x_tran = X.transpose()
          x_j = x_tran[self.j_]
  
          def apply(x):
              return self.sign_ if x >= self.threshold_ else -self.sign_
  
          return np.array(list(map(apply, x_j)))
  
      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`
          """
          a_pred = np.ones(len(labels)) * sign
  
          a = np.dstack((values, labels))[0]
          b = a[a[:, 0].argsort()]
          values = b.T[0]
          labels = b.T[1]
          def mini_pred(X, thr, i):
              # x_tran = X.transpose()
              # x_j = x_tran
              if i == 0:
                  return a_pred
  
              def apply(x):
                  return sign if x >= thr else -sign
  
              a_pred[i - 1] = -sign
              return a_pred
  
          test_values = np.hstack((values, np.array([values[-1].item() + EPSILON], dtype=object)))
          thr_err = np.zeros(len(test_values))
          for i in range(len(test_values)):
              thr_err[i] = weighted_misclassification_error(labels, mini_pred(values, test_values[i], i))
          min_ind = np.argmin(thr_err)
          return test_values[min_ind], thr_err[min_ind]
  
      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
          """
          return weighted_misclassification_error(y, self.predict(X))
  