





"""simple docstring"""





import matplotlib.pyplot as plt
import numpy as np




def 		lowerCAmelCase_     (  lowercase_       :							np.ndarray			,				lowercase_       :							np.ndarray			,				lowercase_       :							float		):

 '''simple docstring'''






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

 return weights




def 		lowerCAmelCase_     (  lowercase_       :							np.ndarray			,				lowercase_       :							np.ndarray			,				lowercase_       :							np.ndarray			,				lowercase_       :							float		):

 '''simple docstring'''






 __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	weight_matrix(lowercase_			,				lowercase_			,				lowercase_		)
 __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	np.linalg.inv(x_train.T @ weight_mat @ x_train		) @ (
     x_train.T @ weight_mat @ y_train.T
 )

 return weight




def 		lowerCAmelCase_     (  lowercase_       :							np.ndarray			,				lowercase_       :							np.ndarray			,				lowercase_       :							float		):

 '''simple docstring'''






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

 return y_pred




def 		lowerCAmelCase_     (  lowercase_       :							str			,				lowercase_       :							str			,				lowercase_       :							str		):

 '''simple docstring'''






 import seaborn as sns

 __SCREAMING_SNAKE_CASE			:      int 							=	sns.load_dataset(lowercase_		)
 __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	np.array(data[x_name]		)
 __SCREAMING_SNAKE_CASE			:      List[Any] 							=	np.array(data[y_name]		)

 __SCREAMING_SNAKE_CASE			:      List[str] 							=	np.ones(len(lowercase_		)		)

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

 return x_train, x_data, y_data




def 		lowerCAmelCase_     (  lowercase_       :							np.ndarray			,				lowercase_       :							np.ndarray			,				lowercase_       :							np.ndarray			,				lowercase_       :							np.ndarray			,				lowercase_       :							str			,				lowercase_       :							str			,				):

 '''simple docstring'''






 __SCREAMING_SNAKE_CASE			:      int 							=	np.sort(lowercase_			,				axis=0		)
 plt.scatter(lowercase_			,				lowercase_			,				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(lowercase_		)
 plt.ylabel(lowercase_		)
 plt.show()


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    # Demo with a dataset from the seaborn module
    _lowerCamelCase					,		_lowerCamelCase					,		_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''')








"""simple docstring"""





import math





class       snake_case		:

      def __init__(      self       :Optional[Any]						,							_lowerCamelCase       :Dict						):
       __SCREAMING_SNAKE_CASE			:      str 							=	len(_lowerCamelCase						)
       __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	[0] * (
           4 * self.N
       )  # approximate the overall size of segment tree with array N
       self.build(1						,							0						,							self.N - 1						)

      def 						SCREAMING_SNAKE_CASE_      (      self       :Union[str, Any]						,							_lowerCamelCase       :List[str]						):
       return idx * 2

      def 						SCREAMING_SNAKE_CASE_      (      self       :Tuple						,							_lowerCamelCase       :Optional[Any]						):
       return idx * 2 + 1

      def 						SCREAMING_SNAKE_CASE_      (      self       :int						,							_lowerCamelCase       :Optional[Any]						,							_lowerCamelCase       :Union[str, Any]						,							_lowerCamelCase       :str						):  # noqa: E741
       if l == r:
        __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	A[l]
       else:
        __SCREAMING_SNAKE_CASE			:      Dict 							=	(l + r) // 2
        self.build(self.left(_lowerCamelCase						)						,							_lowerCamelCase						,							_lowerCamelCase						)
        self.build(self.right(_lowerCamelCase						)						,							mid + 1						,							_lowerCamelCase						)
        __SCREAMING_SNAKE_CASE			:      List[Any] 							=	max(self.st[self.left(_lowerCamelCase						)]						,							self.st[self.right(_lowerCamelCase						)]						)

      def 						SCREAMING_SNAKE_CASE_      (      self       :Tuple						,							_lowerCamelCase       :Optional[Any]						,							_lowerCamelCase       :Optional[Any]						,							_lowerCamelCase       :Union[str, Any]						):
       return self.update_recursive(1						,							0						,							self.N - 1						,							a - 1						,							b - 1						,							_lowerCamelCase						)

      def 						SCREAMING_SNAKE_CASE_      (      self       :Optional[int]						,							_lowerCamelCase       :Optional[Any]						,							_lowerCamelCase       :Any						,							_lowerCamelCase       :Union[str, Any]						,							_lowerCamelCase       :Optional[Any]						,							_lowerCamelCase       :str						,							_lowerCamelCase       :Optional[Any]						):  # noqa: E741
       if r < a or l > b:
        return True
       if l == r:
        __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	val
        return True
       __SCREAMING_SNAKE_CASE			:      List[Any] 							=	(l + r) // 2
       self.update_recursive(self.left(_lowerCamelCase						)						,							_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						)
       self.update_recursive(self.right(_lowerCamelCase						)						,							mid + 1						,							_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						)
       __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	max(self.st[self.left(_lowerCamelCase						)]						,							self.st[self.right(_lowerCamelCase						)]						)
       return True

      def 						SCREAMING_SNAKE_CASE_      (      self       :Tuple						,							_lowerCamelCase       :str						,							_lowerCamelCase       :Any						):
       return self.query_recursive(1						,							0						,							self.N - 1						,							a - 1						,							b - 1						)

      def 						SCREAMING_SNAKE_CASE_      (      self       :str						,							_lowerCamelCase       :Dict						,							_lowerCamelCase       :str						,							_lowerCamelCase       :Union[str, Any]						,							_lowerCamelCase       :Optional[Any]						,							_lowerCamelCase       :Any						):  # noqa: E741
       if r < a or l > b:
        return -math.inf
       if l >= a and r <= b:
        return self.st[idx]
       __SCREAMING_SNAKE_CASE			:      List[str] 							=	(l + r) // 2
       __SCREAMING_SNAKE_CASE			:      Any 							=	self.query_recursive(self.left(_lowerCamelCase						)						,							_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						)
       __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	self.query_recursive(self.right(_lowerCamelCase						)						,							mid + 1						,							_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						)
       return max(_lowerCamelCase						,							_lowerCamelCase						)



      def 						SCREAMING_SNAKE_CASE_      (      self       :Dict						):
       __SCREAMING_SNAKE_CASE			:      str 							=	[]
       for i in range(1						,							N + 1						):
        show_list += [self.query(_lowerCamelCase						,							_lowerCamelCase						)]
       print(_lowerCamelCase						)


if __name__ == "__main__":
    _lowerCamelCase  					=     [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
    _lowerCamelCase  					=     15
    _lowerCamelCase  					=     SegmentTree(A)
    print(segt.query(4, 6))
    print(segt.query(7, 11))
    print(segt.query(7, 12))
    segt.update(1, 3, 1_11)
    print(segt.query(1, 15))
    segt.update(7, 8, 2_35)
    segt.show_data()

