






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""")














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''')






