code: 
  
  
  
  
  
  
  import matplotlib.pyplot as plt
  import numpy as np
  
  
  
  
  
  def    _lowerCamelCase	(	__lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase					)   -> np.ndarray:
  
       '''simple docstring'''
       UpperCAmelCase__			:     List[str]										= len(__lowerCamelCase					)  # Number of training samples
       UpperCAmelCase__			:     Optional[Any]										= np.eye(__lowerCamelCase					)  # Initialize weights as identity matrix
       for j in range(__lowerCamelCase					):
            UpperCAmelCase__			:     Union[str, Any]										= point - x_train[j]
            UpperCAmelCase__			:     Dict										= np.exp(diff @ diff.T / (-2.0 * tau**2)					)
  
       return weights
  
  
  
  
  
  def    _lowerCamelCase	(	__lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase					)   -> np.ndarray:
  
       '''simple docstring'''
       UpperCAmelCase__			:     Dict										= weight_matrix(__lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase					)
       UpperCAmelCase__			:     Tuple										= np.linalg.inv(x_train.T @ weight_mat @ x_train					) @ (
           x_train.T @ weight_mat @ y_train.T
       )
  
       return weight
  
  
  
  
  
  def    _lowerCamelCase	(	__lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase					)   -> np.ndarray:
  
       '''simple docstring'''
       UpperCAmelCase__			:     Union[str, Any]										= np.zeros(len(__lowerCamelCase					)					)  # Initialize array of predictions
       for i, item in enumerate(__lowerCamelCase					):
            UpperCAmelCase__			:     List[Any]										= item @ local_weight(__lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase					)
  
       return y_pred
  
  
  
  
  
  def    _lowerCamelCase	(	__lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase					)   -> tuple[np.ndarray, np.ndarray, np.ndarray]:
  
       '''simple docstring'''
       import seaborn as sns
  
       UpperCAmelCase__			:     Union[str, Any]										= sns.load_dataset(__lowerCamelCase					)
       UpperCAmelCase__			:     List[str]										= np.array(data[x_name]					)
       UpperCAmelCase__			:     Dict										= np.array(data[y_name]					)
  
       UpperCAmelCase__			:     str										= np.ones(len(__lowerCamelCase					)					)
  
       # pairing elements of one and x_data
       UpperCAmelCase__			:     List[str]										= np.column_stack((one, x_data)					)
  
       return x_train, x_data, y_data
  
  
  
  
  
  def    _lowerCamelCase	(	__lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase   ,       )   -> None:
  
       '''simple docstring'''
       UpperCAmelCase__			:     Optional[int]										= 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
        SCREAMING_SNAKE_CASE__							, SCREAMING_SNAKE_CASE__							, SCREAMING_SNAKE_CASE__		:       str   							=							load_data("""tips""", """total_bill""", """tip""")
        SCREAMING_SNAKE_CASE__		:       Union[str, Any]   							=							local_weight_regression(training_data_x, tip, 5)
        plot_preds(training_data_x, predictions, total_bill, tip, """total_bill""", """tip""")
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  from .stack import Stack
  
  
  
  
  
  def    _lowerCamelCase	(	__lowerCamelCase					)   -> bool:
  
       '''simple docstring'''
       UpperCAmelCase__			:     Stack[str]										= Stack()
       UpperCAmelCase__			:     str										= {"""(""": """)""", """[""": """]""", """{""": """}"""}
       for bracket in parentheses:
            if bracket in bracket_pairs:
                 stack.push(__lowerCamelCase					)
            elif bracket in (")", "]", "}"):
                 if stack.is_empty() or bracket_pairs[stack.pop()] != bracket:
                      return False
       return stack.is_empty()
  
  
  if __name__ == "__main__":
        from doctest import testmod
  
        testmod()
  
        SCREAMING_SNAKE_CASE__		:       Any   							=							["""((()))""", """((())""", """(()))"""]
        print("""Balanced parentheses demonstration:\n""")
        for example in examples:
              SCREAMING_SNAKE_CASE__		:       List[str]   							=							"""""" if balanced_parentheses(example) else """not """
              print(f'''{example} is {not_str}balanced''')
  
  
  
  
  
  
  