


import matplotlib.pyplot as plt
import numpy as np


def 	_UpperCamelCase							(				lowercase__ ,	lowercase__ ,	lowercase__				):
						__SCREAMING_SNAKE_CASE						:					Any		      =		len(_UpperCAmelCase				)  # Number of training samples
						__SCREAMING_SNAKE_CASE						:					int		      =		np.eye(_UpperCAmelCase				)  # Initialize weights as identity matrix
						for j in range(_UpperCAmelCase				):
												__SCREAMING_SNAKE_CASE						:					int		      =		point - x_train[j]
												__SCREAMING_SNAKE_CASE						:					Optional[Any]		      =		np.exp(diff @ diff.T / (-2.0 * tau**2)				)

						return weights


def 	_UpperCamelCase							(				lowercase__ ,	lowercase__ ,	lowercase__ ,	lowercase__				):
						__SCREAMING_SNAKE_CASE						:					str		      =		weight_matrix(_UpperCAmelCase ,	_UpperCAmelCase ,	_UpperCAmelCase				)
						__SCREAMING_SNAKE_CASE						:					str		      =		np.linalg.inv(x_train.T @ weight_mat @ x_train				) @ (
						    x_train.T @ weight_mat @ y_train.T
						)

						return weight


def 	_UpperCamelCase							(				lowercase__ ,	lowercase__ ,	lowercase__				):
						__SCREAMING_SNAKE_CASE						:					Any		      =		np.zeros(len(_UpperCAmelCase				)				)  # Initialize array of predictions
						for i, item in enumerate(_UpperCAmelCase				):
												__SCREAMING_SNAKE_CASE						:					Optional[int]		      =		item @ local_weight(_UpperCAmelCase ,	_UpperCAmelCase ,	_UpperCAmelCase ,	_UpperCAmelCase				)

						return y_pred


def 	_UpperCamelCase							(				lowercase__ ,	lowercase__ ,	lowercase__				):
						import seaborn as sns

						__SCREAMING_SNAKE_CASE						:					List[Any]		      =		sns.load_dataset(_UpperCAmelCase				)
						__SCREAMING_SNAKE_CASE						:					List[str]		      =		np.array(data[x_name]				)
						__SCREAMING_SNAKE_CASE						:					Optional[int]		      =		np.array(data[y_name]				)

						__SCREAMING_SNAKE_CASE						:					Dict		      =		np.ones(len(_UpperCAmelCase				)				)

						# pairing elements of one and x_data
						__SCREAMING_SNAKE_CASE						:					Any		      =		np.column_stack((one, x_data)				)

						return x_train, x_data, y_data


def 	_UpperCamelCase							(				lowercase__ ,	lowercase__ ,	lowercase__ ,	lowercase__ ,	lowercase__ ,	lowercase__ ,	):
						__SCREAMING_SNAKE_CASE						:					Optional[int]		      =		np.sort(_UpperCAmelCase ,	axis=0				)
						plt.scatter(_UpperCAmelCase ,	_UpperCAmelCase ,	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(_UpperCAmelCase				)
						plt.ylabel(_UpperCAmelCase				)
						plt.show()


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						# Demo with a dataset from the seaborn module
						__lowerCAmelCase     :			List[Any]      =load_data('tips', 'total_bill', 'tip')
						__lowerCAmelCase     :			int      =local_weight_regression(training_data_x, tip, 5)
						plot_preds(training_data_x, predictions, total_bill, tip, 'total_bill', 'tip')




from __future__ import annotations


def 	_UpperCamelCase							(				lowercase__				):
						__SCREAMING_SNAKE_CASE						:					List[Any]		      =		sorted(lowercase__				)
						__SCREAMING_SNAKE_CASE						:					str		      =		len(lowercase__				)
						__SCREAMING_SNAKE_CASE						:					Union[str, Any]		      =		length >> 1
						return (
						    (sorted_list[mid_index] + sorted_list[mid_index - 1]) / 2
						    if length % 2 == 0
						    else sorted_list[mid_index]
						)


def 	_UpperCamelCase							(				):
						import doctest

						doctest.testmod()


if __name__ == "__main__":
						main()
