





'''simple docstring'''

import matplotlib.pyplot as plt
import numpy as np




def  _a     (				lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_						):





      """simple docstring"""



      _snake_case		:						Optional[int]         =  len(lowerCAmelCase_						)  # Number of training samples
      _snake_case		:						int         =  np.eye(lowerCAmelCase_						)  # Initialize weights as identity matrix
      for j in range(lowerCAmelCase_						):
            _snake_case		:						Optional[int]         =  point - x_train[j]
            _snake_case		:						Any         =  np.exp(diff @ diff.T / (-2.0 * tau**2)						)

      return weights




def  _a     (				lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_						):





      """simple docstring"""



      _snake_case		:						Optional[int]         =  weight_matrix(lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_						)
      _snake_case		:						List[str]         =  np.linalg.inv(x_train.T @ weight_mat @ x_train						) @ (
          x_train.T @ weight_mat @ y_train.T
      )

      return weight




def  _a     (				lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_						):





      """simple docstring"""



      _snake_case		:						List[Any]         =  np.zeros(len(lowerCAmelCase_						)						)  # Initialize array of predictions
      for i, item in enumerate(lowerCAmelCase_						):
            _snake_case		:						List[Any]         =  item @ local_weight(lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_						)

      return y_pred




def  _a     (				lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_						):





      """simple docstring"""



      import seaborn as sns

      _snake_case		:						int         =  sns.load_dataset(lowerCAmelCase_						)
      _snake_case		:						List[str]         =  np.array(data[x_name]						)
      _snake_case		:						Any         =  np.array(data[y_name]						)

      _snake_case		:						Dict         =  np.ones(len(lowerCAmelCase_						)						)

      # pairing elements of one and x_data
      _snake_case		:						List[Any]         =  np.column_stack((one, x_data)						)

      return x_train, x_data, y_data




def  _a     (				lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   ):





      """simple docstring"""



      _snake_case		:						Union[str, Any]         =  np.sort(lowerCAmelCase_      ,   axis=0						)
      plt.scatter(lowerCAmelCase_      ,   lowerCAmelCase_      ,   color='''blue'''						)
      plt.plot(
          x_train_sorted[:, 1]      ,   preds[x_train[:, 1].argsort(0						)]      ,   color='''yellow'''      ,   linewidth=5      ,   )
      plt.title('''Local Weighted Regression'''						)
      plt.xlabel(lowerCAmelCase_						)
      plt.ylabel(lowerCAmelCase_						)
      plt.show()


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   # Demo with a dataset from the seaborn module
   UpperCAmelCase,							UpperCAmelCase,							UpperCAmelCase       :		List[Any]		=				load_data('tips', 'total_bill', 'tip')
   UpperCAmelCase       :		int		=				local_weight_regression(training_data_x, tip, 5)
   plot_preds(training_data_x, predictions, total_bill, tip, 'total_bill', 'tip')









'''simple docstring'''

import math




def  _a     (				lowerCAmelCase_						):





      """simple docstring"""



      if 1 < number < 4:
            # 2 and 3 are primes
            return True
      elif number < 2 or number % 2 == 0 or number % 3 == 0:
            # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
            return False

      # All primes number are in format of 6k +/- 1
      for i in range(5      ,   int(math.sqrt(lowerCAmelCase_						) + 1						)      ,   6						):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True




def  _a     (				lowerCAmelCase_ = 2_000_000						):





      """simple docstring"""



      return sum(num for num in range(3      ,   lowerCAmelCase_      ,   2						) if is_prime(lowerCAmelCase_						)						) + 2 if n > 2 else 0


if __name__ == "__main__":
   print(F"""{solution() = }""")


