


import matplotlib.pyplot as plt
import numpy as np
def 							_UpperCAmelCase    (UpperCamelCase__					:  Optional[Any]    ,							UpperCamelCase__					:  List[str]    ,							UpperCamelCase__					:  Union[str, Any]						):
       _A				:	List[str]       =			len(UpperCamelCase__						)  # Number of training samples
       _A				:	int       =			np.eye(UpperCamelCase__						)  # Initialize weights as identity matrix
       for j in range(UpperCamelCase__						):
              _A				:	List[Any]       =			point - x_train[j]
              _A				:	Union[str, Any]       =			np.exp(diff @ diff.T / (-2.0 * tau**2)						)

       return weights
def 							_UpperCAmelCase    (UpperCamelCase__					:  Optional[Any]    ,							UpperCamelCase__					:  Dict    ,							UpperCamelCase__					:  Union[str, Any]    ,							UpperCamelCase__					:  Optional[Any]						):
       _A				:	Optional[int]       =			weight_matrix(UpperCamelCase__    ,							UpperCamelCase__    ,							UpperCamelCase__						)
       _A				:	Union[str, Any]       =			np.linalg.inv(x_train.T @ weight_mat @ x_train						) @ (
           x_train.T @ weight_mat @ y_train.T
       )

       return weight
def 							_UpperCAmelCase    (UpperCamelCase__					:  Dict    ,							UpperCamelCase__					:  str    ,							UpperCamelCase__					:  Optional[Any]						):
       _A				:	Union[str, Any]       =			np.zeros(len(UpperCamelCase__						)						)  # Initialize array of predictions
       for i, item in enumerate(UpperCamelCase__						):
              _A				:	Optional[int]       =			item @ local_weight(UpperCamelCase__    ,							UpperCamelCase__    ,							UpperCamelCase__    ,							UpperCamelCase__						)

       return y_pred
def 							_UpperCAmelCase    (UpperCamelCase__					:  Any    ,							UpperCamelCase__					:  List[str]    ,							UpperCamelCase__					:  int						):
       import seaborn as sns

       _A				:	Optional[int]       =			sns.load_dataset(UpperCamelCase__						)
       _A				:	Tuple       =			np.array(data[x_name]						)
       _A				:	Tuple       =			np.array(data[y_name]						)

       _A				:	Any       =			np.ones(len(UpperCamelCase__						)						)

       # pairing elements of one and x_data
       _A				:	Dict       =			np.column_stack((one, x_data)						)

       return x_train, x_data, y_data
def 							_UpperCAmelCase    (UpperCamelCase__					:  Dict    ,							UpperCamelCase__					:  int    ,							UpperCamelCase__					:  Tuple    ,							UpperCamelCase__					:  Tuple    ,							UpperCamelCase__					:  List[str]    ,							UpperCamelCase__					:  List[Any]    ,							):
       _A				:	str       =			np.sort(UpperCamelCase__    ,							axis=0						)
       plt.scatter(UpperCamelCase__    ,							UpperCamelCase__    ,							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(UpperCamelCase__						)
       plt.ylabel(UpperCamelCase__						)
       plt.show()


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    # Demo with a dataset from the seaborn module
    lowerCAmelCase__						=			load_data('tips', 'total_bill', 'tip')
    lowerCAmelCase__						=			local_weight_regression(training_data_x, tip, 5)
    plot_preds(training_data_x, predictions, total_bill, tip, 'total_bill', 'tip')




from __future__ import annotations

from typing import Any







class 					lowerCAmelCase__	:




     '''simple docstring'''


     def __init__(						self			,						__lowerCamelCase			,						__lowerCamelCase)      ->    None:  # noqa: A002
            _A				:	List[str]       =			item
            _A				:	List[Any]       =			next







class 					lowerCAmelCase__	:




     '''simple docstring'''


     def __init__(						self)      ->    None:
            _A				:	Node | None       =			None
            _A				:	List[Any]       =			0


     def 			_lowerCamelCase			(						self			,						__lowerCamelCase)      ->    None:
            _A				:	Union[str, Any]       =			Node(__lowerCamelCase			,						self.head)
            self.size += 1


     def 			_lowerCamelCase			(						self)      ->    Any:
            # Switched 'self.is_empty()' to 'self.head is None'
            # because mypy was considering the possibility that 'self.head'
            # can be None in below else part and giving error
            if self.head is None:
                   return None
            else:
                   _A				:	str       =			self.head.item
                   _A				:	List[Any]       =			self.head.next
                   self.size -= 1
                   return item


     def 			_lowerCamelCase			(						self)      ->    bool:
            return self.head is None


     def __str__(						self)      ->    str:
            if self.is_empty():
                   return ""
            else:
                   _A				:	List[str]       =			self.head
                   _A				:	Optional[int]       =			""
                   _A				:	list[str]       =			[]
                   while iterate:
                          item_list.append(str(iterate.item))
                          _A				:	Optional[Any]       =			iterate.next

                   _A				:	List[str]       =			" --> ".join(__lowerCamelCase)

                   return item_str


     def __len__(						self)      ->    int:
            return self.size
