code: 
  """simple docstring"""
  
  
  
  
  
  import matplotlib.pyplot as plt
  import numpy as np
  
  
  
  
  
  
  
  def 			__a  (	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						):
     UpperCAmelCase_      :      List[str]      =					len(__lowerCamelCase						)  # Number of training samples
     UpperCAmelCase_      :      Optional[int]      =					np.eye(__lowerCamelCase						)  # Initialize weights as identity matrix
     for j in range(__lowerCamelCase						):
        UpperCAmelCase_      :      Optional[int]      =					point - x_train[j]
        UpperCAmelCase_      :      Any      =					np.exp(diff @ diff.T / (-2.0 * tau**2)						)
  
     return weights
  
  
  
  
  
  
  
  def 			__a  (	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						):
     UpperCAmelCase_      :      Optional[Any]      =					weight_matrix(__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						)
     UpperCAmelCase_      :      Optional[int]      =					np.linalg.inv(x_train.T @ weight_mat @ x_train						) @ (
         x_train.T @ weight_mat @ y_train.T
     )
  
     return weight
  
  
  
  
  
  
  
  def 			__a  (	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						):
     UpperCAmelCase_      :      Optional[Any]      =					np.zeros(len(__lowerCamelCase						)						)  # Initialize array of predictions
     for i, item in enumerate(__lowerCamelCase						):
        UpperCAmelCase_      :      Dict      =					item @ local_weight(__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						)
  
     return y_pred
  
  
  
  
  
  
  
  def 			__a  (	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						):
     import seaborn as sns
  
     UpperCAmelCase_      :      List[str]      =					sns.load_dataset(__lowerCamelCase						)
     UpperCAmelCase_      :      List[Any]      =					np.array(data[x_name]						)
     UpperCAmelCase_      :      Union[str, Any]      =					np.array(data[y_name]						)
  
     UpperCAmelCase_      :      Optional[Any]      =					np.ones(len(__lowerCamelCase						)						)
  
     # pairing elements of one and x_data
     UpperCAmelCase_      :      Union[str, Any]      =					np.column_stack((one, x_data)						)
  
     return x_train, x_data, y_data
  
  
  
  
  
  
  
  def 			__a  (	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	):
     UpperCAmelCase_      :      Union[str, Any]      =					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
      _a ,			_a ,			_a	 =							load_data('tips', 'total_bill', 'tip')
      _a	 =							local_weight_regression(training_data_x, tip, 5)
      plot_preds(training_data_x, predictions, total_bill, tip, 'total_bill', 'tip')
  
  
  
style_context: 
  """simple docstring"""
  
  
  
  
  
  from __future__ import annotations
  
  from typing import Any
  
  
  class A_			:
  
  
  
  
    '''simple docstring'''
  
  
  
  
  
  
  
    def __init__(	self       ,     lowercase_       ,     lowercase_						):  # noqa: A002
  
       """simple docstring"""
       UpperCAmelCase_      :      Optional[Any]      =					item
       UpperCAmelCase_      :      Optional[Any]      =					next
  
  
  
  
  class A_			:
  
  
  
  
    '''simple docstring'''
  
  
  
  
  
  
  
    def __init__(	self						):
  
       """simple docstring"""
       UpperCAmelCase_      :      Node | None      =					None
       UpperCAmelCase_      :      Optional[int]      =					0
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self       ,     lowercase_						):
  
       """simple docstring"""
       UpperCAmelCase_      :      int      =					Node(lowercase_       ,     self.head						)
       self.size += 1
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self						):
  
       """simple docstring"""
       # 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:
          UpperCAmelCase_      :      int      =					self.head.item
          UpperCAmelCase_      :      str      =					self.head.next
          self.size -= 1
          return item
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self						):
  
       """simple docstring"""
       return self.head is None
  
  
  
  
  
  
  
    def __str__(	self						):
  
       """simple docstring"""
       if self.is_empty():
          return ""
       else:
          UpperCAmelCase_      :      str      =					self.head
          UpperCAmelCase_      :      str      =					""
          UpperCAmelCase_      :      list[str]      =					[]
          while iterate:
             item_list.append(str(iterate.item						)						)
             UpperCAmelCase_      :      Tuple      =					iterate.next
  
          UpperCAmelCase_      :      Optional[Any]      =					" --> ".join(lowercase_						)
  
          return item_str
  
  
  
  
  
  
  
    def __len__(	self						):
  
       """simple docstring"""
       return self.size
  
  
  