



'''simple docstring'''





import matplotlib.pyplot as plt
import numpy as np



def     UpperCAmelCase     (    a_      ,		a_      ,		a_		)   ->       Optional[Any]:



   """simple docstring"""






   A_  :		int						=					len(a_		)  # Number of training samples
   A_  :		str						=					np.eye(a_		)  # Initialize weights as identity matrix
   for j in range(a_		):
      A_  :		str						=					point - x_train[j]
      A_  :		int						=					np.exp(diff @ diff.T / (-2.0 * tau**2)		)

   return weights



def     UpperCAmelCase     (    a_      ,		a_      ,		a_      ,		a_		)   ->       int:



   """simple docstring"""






   A_  :		List[str]						=					weight_matrix(a_      ,		a_      ,		a_		)
   A_  :		Any						=					np.linalg.inv(x_train.T @ weight_mat @ x_train		) @ (
       x_train.T @ weight_mat @ y_train.T
   )

   return weight



def     UpperCAmelCase     (    a_      ,		a_      ,		a_		)   ->       str:



   """simple docstring"""






   A_  :		Union[str, Any]						=					np.zeros(len(a_		)		)  # Initialize array of predictions
   for i, item in enumerate(a_		):
      A_  :		str						=					item @ local_weight(a_      ,		a_      ,		a_      ,		a_		)

   return y_pred



def     UpperCAmelCase     (    a_      ,		a_      ,		a_		)   ->       str:



   """simple docstring"""






   import seaborn as sns

   A_  :		Optional[int]						=					sns.load_dataset(a_		)
   A_  :		Any						=					np.array(data[x_name]		)
   A_  :		Optional[int]						=					np.array(data[y_name]		)

   A_  :		List[str]						=					np.ones(len(a_		)		)

   # pairing elements of one and x_data
   A_  :		int						=					np.column_stack((one, x_data)		)

   return x_train, x_data, y_data



def     UpperCAmelCase     (    a_      ,		a_      ,		a_      ,		a_      ,		a_      ,		a_      ,		)   ->       List[str]:



   """simple docstring"""






   A_  :		Tuple						=					np.sort(a_      ,		axis=0		)
   plt.scatter(a_      ,		a_      ,		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(a_		)
   plt.ylabel(a_		)
   plt.show()


if __name__ == "__main__":
  import doctest

  doctest.testmod()

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







import matplotlib.pyplot as plt
import numpy as np




def  A_(      A					,   A					,   A ):
	UpperCAmelCase_		    =  len(A )  # Number of training samples
	UpperCAmelCase_		    =  np.eye(A )  # Initialize weights as identity matrix
	for j in range(A ):
		UpperCAmelCase_		    =  point - x_train[j]
		UpperCAmelCase_		    =  np.exp(diff @ diff.T / (-2.0 * tau**2) )

	return weights




def  A_(      A					,   A					,   A					,   A ):
	UpperCAmelCase_		    =  weight_matrix(A					,   A					,   A )
	UpperCAmelCase_		    =  np.linalg.inv(x_train.T @ weight_mat @ x_train ) @ (
	    x_train.T @ weight_mat @ y_train.T
	)

	return weight




def  A_(      A					,   A					,   A ):
	UpperCAmelCase_		    =  np.zeros(len(A ) )  # Initialize array of predictions
	for i, item in enumerate(A ):
		UpperCAmelCase_		    =  item @ local_weight(A					,   A					,   A					,   A )

	return y_pred




def  A_(      A					,   A					,   A ):
	import seaborn as sns

	UpperCAmelCase_		    =  sns.load_dataset(A )
	UpperCAmelCase_		    =  np.array(data[x_name] )
	UpperCAmelCase_		    =  np.array(data[y_name] )

	UpperCAmelCase_		    =  np.ones(len(A ) )

	# pairing elements of one and x_data
	UpperCAmelCase_		    =  np.column_stack((one, x_data) )

	return x_train, x_data, y_data




def  A_(      A					,   A					,   A					,   A					,   A					,   A					,   ):
	UpperCAmelCase_		    =  np.sort(A					,   axis=0 )
	plt.scatter(A					,   A					,   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(A )
	plt.ylabel(A )
	plt.show()


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				# Demo with a dataset from the seaborn module
				UpperCamelCase__	,      UpperCamelCase__	,      UpperCamelCase__ :			Tuple       	=			load_data("""tips""", """total_bill""", """tip""")
				UpperCamelCase__ :			Tuple       	=			local_weight_regression(training_data_x, tip, 5)
				plot_preds(training_data_x, predictions, total_bill, tip, """total_bill""", """tip""")


