"""simple docstring"""







import matplotlib.pyplot as plt
import numpy as np




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				np.ndarray  ,       _SCREAMING_SNAKE_CASE				:				np.ndarray  ,       _SCREAMING_SNAKE_CASE				:				float						)    ->     np.ndarray:







     '''simple docstring'''


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

     return weights




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				np.ndarray  ,       _SCREAMING_SNAKE_CASE				:				np.ndarray  ,       _SCREAMING_SNAKE_CASE				:				np.ndarray  ,       _SCREAMING_SNAKE_CASE				:				float						)    ->     np.ndarray:







     '''simple docstring'''


     __A					:					Tuple								=		weight_matrix(_SCREAMING_SNAKE_CASE  ,       _SCREAMING_SNAKE_CASE  ,       _SCREAMING_SNAKE_CASE						)
     __A					:					List[Any]								=		np.linalg.inv(x_train.T @ weight_mat @ x_train						) @ (
         x_train.T @ weight_mat @ y_train.T
     )

     return weight




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				np.ndarray  ,       _SCREAMING_SNAKE_CASE				:				np.ndarray  ,       _SCREAMING_SNAKE_CASE				:				float						)    ->     np.ndarray:







     '''simple docstring'''


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

     return y_pred




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				str  ,       _SCREAMING_SNAKE_CASE				:				str  ,       _SCREAMING_SNAKE_CASE				:				str						)    ->     tuple[np.ndarray, np.ndarray, np.ndarray]:







     '''simple docstring'''


     import seaborn as sns

     __A					:					Union[str, Any]								=		sns.load_dataset(_SCREAMING_SNAKE_CASE						)
     __A					:					Optional[int]								=		np.array(data[x_name]						)
     __A					:					str								=		np.array(data[y_name]						)

     __A					:					List[Any]								=		np.ones(len(_SCREAMING_SNAKE_CASE						)						)

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

     return x_train, x_data, y_data




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				np.ndarray  ,       _SCREAMING_SNAKE_CASE				:				np.ndarray  ,       _SCREAMING_SNAKE_CASE				:				np.ndarray  ,       _SCREAMING_SNAKE_CASE				:				np.ndarray  ,       _SCREAMING_SNAKE_CASE				:				str  ,       _SCREAMING_SNAKE_CASE				:				str  ,       )    ->     None:







     '''simple docstring'''


     __A					:					int								=		np.sort(_SCREAMING_SNAKE_CASE  ,       axis=0						)
     plt.scatter(_SCREAMING_SNAKE_CASE  ,       _SCREAMING_SNAKE_CASE  ,       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(_SCREAMING_SNAKE_CASE						)
     plt.ylabel(_SCREAMING_SNAKE_CASE						)
     plt.show()


if __name__ == "__main__":
       import doctest

       doctest.testmod()

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




"""simple docstring"""







def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				list[int]						)    ->     tuple[int, int]:







     '''simple docstring'''


     if len(_SCREAMING_SNAKE_CASE						) == 1:
          return a[0], a[0]
     else:
          # split A into half.
          __A					:					List[str]								=		a[: len(_SCREAMING_SNAKE_CASE						) // 2]
          __A					:					Optional[Any]								=		a[len(_SCREAMING_SNAKE_CASE						) // 2 :]

          # 2 sub problems, 1/2 of original size.
          __A						,		__A					:					int								=		max_difference(_SCREAMING_SNAKE_CASE						)
          __A						,		__A					:					str								=		max_difference(_SCREAMING_SNAKE_CASE						)

          # get min of first and max of second
          # linear time
          __A					:					str								=		min(_SCREAMING_SNAKE_CASE						)
          __A					:					Optional[int]								=		max(_SCREAMING_SNAKE_CASE						)

          # 3 cases, either (small1, big1),
          # (min_first, max_second), (small2, big2)
          # constant comparisons
          if biga - smalla > max_second - min_first and biga - smalla > biga - smalla:
               return smalla, biga
          elif biga - smalla > max_second - min_first:
               return smalla, biga
          else:
               return min_first, max_second


if __name__ == "__main__":
       import doctest

       doctest.testmod()



