code: 
  
  
  '''simple docstring'''
  
  import matplotlib.pyplot as plt
  import numpy as np
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			np.ndarray	,	lowerCAmelCase       :			np.ndarray	,	lowerCAmelCase       :			float	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	__magic_name__ :					Union[str, Any]  			=  len(lowerCAmelCase	)  # Number of training samples
  	__magic_name__ :					Optional[Any]  			=  np.eye(lowerCAmelCase	)  # Initialize weights as identity matrix
  	for j in range(lowerCAmelCase	):
  		__magic_name__ :					Optional[Any]  			=  point - x_train[j]
  		__magic_name__ :					Optional[int]  			=  np.exp(diff @ diff.T / (-2.0 * tau**2)	)
  
  	return weights
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			np.ndarray	,	lowerCAmelCase       :			np.ndarray	,	lowerCAmelCase       :			np.ndarray	,	lowerCAmelCase       :			float	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	__magic_name__ :					Dict  			=  weight_matrix(lowerCAmelCase	,	lowerCAmelCase	,	lowerCAmelCase	)
  	__magic_name__ :					Dict  			=  np.linalg.inv(x_train.T @ weight_mat @ x_train	) @ (
  	    x_train.T @ weight_mat @ y_train.T
  	)
  
  	return weight
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			np.ndarray	,	lowerCAmelCase       :			np.ndarray	,	lowerCAmelCase       :			float	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	__magic_name__ :					Tuple  			=  np.zeros(len(lowerCAmelCase	)	)  # Initialize array of predictions
  	for i, item in enumerate(lowerCAmelCase	):
  		__magic_name__ :					Optional[Any]  			=  item @ local_weight(lowerCAmelCase	,	lowerCAmelCase	,	lowerCAmelCase	,	lowerCAmelCase	)
  
  	return y_pred
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			str	,	lowerCAmelCase       :			str	,	lowerCAmelCase       :			str	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	import seaborn as sns
  
  	__magic_name__ :					Optional[int]  			=  sns.load_dataset(lowerCAmelCase	)
  	__magic_name__ :					Any  			=  np.array(data[x_name]	)
  	__magic_name__ :					List[Any]  			=  np.array(data[y_name]	)
  
  	__magic_name__ :					List[str]  			=  np.ones(len(lowerCAmelCase	)	)
  
  	# pairing elements of one and x_data
  	__magic_name__ :					Tuple  			=  np.column_stack((one, x_data)	)
  
  	return x_train, x_data, y_data
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			np.ndarray	,	lowerCAmelCase       :			np.ndarray	,	lowerCAmelCase       :			np.ndarray	,	lowerCAmelCase       :			np.ndarray	,	lowerCAmelCase       :			str	,	lowerCAmelCase       :			str	,	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	__magic_name__ :					str  			=  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
  							lowerCAmelCase			,					lowerCAmelCase			,					lowerCAmelCase   :Union[str, Any]								=    load_data('''tips''', '''total_bill''', '''tip''')
  							lowerCAmelCase   :Tuple								=    local_weight_regression(training_data_x, tip, 5)
  							plot_preds(training_data_x, predictions, total_bill, tip, '''total_bill''', '''tip''')
style_context: 
  
  
  '''simple docstring'''
  
  import math
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			int	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	if not isinstance(lowerCAmelCase	,	lowerCAmelCase	):
  		__magic_name__ :					str  			=  f'Input value of [number={number}] must be an integer'
  		raise TypeError(lowerCAmelCase	)
  	if number < 1:
  		__magic_name__ :					Tuple  			=  f'Input value of [number={number}] must be a positive integer'
  		raise ValueError(lowerCAmelCase	)
  	__magic_name__ :					Tuple  			=  [number]
  	while number != 1:
  		if number % 2 == 0:
  			__magic_name__ :					Optional[int]  			=  math.floor(math.sqrt(lowerCAmelCase	)	)
  		else:
  			__magic_name__ :					Union[str, Any]  			=  math.floor(
  			    math.sqrt(lowerCAmelCase	) * math.sqrt(lowerCAmelCase	) * math.sqrt(lowerCAmelCase	)	)
  		sequence.append(lowerCAmelCase	)
  	return sequence
  
  
  if __name__ == "__main__":
  							import doctest
  
  							doctest.testmod()