





import numpy as np




def  A_(      A ):
	UpperCAmelCase_    ,						UpperCAmelCase_		    =  a.shape
	UpperCAmelCase_		    =  min(A					,   A )
	UpperCAmelCase_		    =  np.eye(A )
	UpperCAmelCase_		    =  a.copy()

	for k in range(t - 1 ):
		# select a column of modified matrix A':
		UpperCAmelCase_		    =  r[k:, [k]]
		# construct first basis vector
		UpperCAmelCase_		    =  np.zeros_like(A )
		UpperCAmelCase_		    =  1.0
		# determine scaling factor
		UpperCAmelCase_		    =  np.linalg.norm(A )
		# construct vector v for Householder reflection
		UpperCAmelCase_		    =  x + np.sign(x[0] ) * alpha * ea
		v /= np.linalg.norm(A )

		# construct the Householder matrix
		UpperCAmelCase_		    =  np.eye(m - k ) - 2.0 * v @ v.T
		# pad with ones and zeros as necessary
		UpperCAmelCase_		    =  np.block([[np.eye(A ), np.zeros((k, m - k) )], [np.zeros((m - k, k) ), q_k]] )

		UpperCAmelCase_		    =  q @ q_k.T
		UpperCAmelCase_		    =  q_k @ r

	return q, r


if __name__ == "__main__":
				import doctest

				doctest.testmod()









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""")


