

import matplotlib.pyplot as plt
import numpy as np



def  __lowerCAmelCase (  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  __lowerCAmelCase (  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  __lowerCAmelCase (  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  __lowerCAmelCase (  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  __lowerCAmelCase (  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
				_a							,     _a							,     _a:      List[str]								=     load_data("""tips""", """total_bill""", """tip""")
				_a:      Any								=     local_weight_regression(training_data_x, tip, 5)
				plot_preds(training_data_x, predictions, total_bill, tip, """total_bill""", """tip""")


def  __lowerCAmelCase (  A      ):
	UpperCAmelCase_    			=     len(A      )

	# Set the gap value to be decreased by a factor of 1.3
	# after each iteration
	UpperCAmelCase_    			=     1.3

	# Continue sorting until the gap is 1
	while gap > 1:
		# Decrease the gap value
		UpperCAmelCase_    			=     int(gap / shrink      )

		# Sort the elements using insertion sort
		for i in range(A    ,       len(A      )      ):
			UpperCAmelCase_    			=     collection[i]
			UpperCAmelCase_    			=     i
			while j >= gap and collection[j - gap] > temp:
				UpperCAmelCase_    			=     collection[j - gap]
				j -= gap
			UpperCAmelCase_    			=     temp

	return collection


if __name__ == "__main__":
				import doctest

				doctest.testmod()