code: 
  
  """simple docstring"""
  
  
  
  
  import matplotlib.pyplot as plt
  import numpy as np
  def      __SCREAMING_SNAKE_CASE		(		lowercase__    ,							lowercase__    ,							lowercase__   ):
  					"""simple docstring"""
  					A    =      len(lowercase__   )  # Number of training samples
  					A    =      np.eye(lowercase__   )  # Initialize weights as identity matrix
  					for j in range(lowercase__   ):
  										A    =      point - x_train[j]
  										A    =      np.exp(diff @ diff.T / (-2.0 * tau**2)   )
  
  					return weights
  def      __SCREAMING_SNAKE_CASE		(		lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__   ):
  					"""simple docstring"""
  					A    =      weight_matrix(lowercase__    ,							lowercase__    ,							lowercase__   )
  					A    =      np.linalg.inv(x_train.T @ weight_mat @ x_train   ) @ (
  					    x_train.T @ weight_mat @ y_train.T
  					)
  
  					return weight
  def      __SCREAMING_SNAKE_CASE		(		lowercase__    ,							lowercase__    ,							lowercase__   ):
  					"""simple docstring"""
  					A    =      np.zeros(len(lowercase__   )   )  # Initialize array of predictions
  					for i, item in enumerate(lowercase__   ):
  										A    =      item @ local_weight(lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__   )
  
  					return y_pred
  def      __SCREAMING_SNAKE_CASE		(		lowercase__    ,							lowercase__    ,							lowercase__   ):
  					"""simple docstring"""
  					import seaborn as sns
  
  					A    =      sns.load_dataset(lowercase__   )
  					A    =      np.array(data[x_name]   )
  					A    =      np.array(data[y_name]   )
  
  					A    =      np.ones(len(lowercase__   )   )
  
  					# pairing elements of one and x_data
  					A    =      np.column_stack((one, x_data)   )
  
  					return x_train, x_data, y_data
  def      __SCREAMING_SNAKE_CASE		(		lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							):
  					"""simple docstring"""
  					A    =      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
  	__A						,					__A						,					__A  :					Optional[Any]												=	load_data('tips', 'total_bill', 'tip')
  	__A  :					Dict												=	local_weight_regression(training_data_x, tip, 5)
  	plot_preds(training_data_x, predictions, total_bill, tip, 'total_bill', 'tip')
  
  
  
  
  
  
style_context: 
  
  """simple docstring"""
  
  
  
  
  def      __SCREAMING_SNAKE_CASE		(		lowercase__   ):
  					"""simple docstring"""
  					if not isinstance(lowercase__    ,							lowercase__   ):
  										raise ValueError("double_factorial() only accepts integral values"   )
  					if n < 0:
  										raise ValueError("double_factorial() not defined for negative values"   )
  					return 1 if n <= 1 else n * double_factorial(n - 2   )
  
  
  if __name__ == "__main__":
  	import doctest
  
  	doctest.testmod()
  
  
  
  
  
  