



import matplotlib.pyplot as plt
import numpy as np


def 		UpperCAmelCase    (			a_	,     a_	,     a_		)	->			np.ndarray:







				"""simple docstring"""



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

				return weights


def 		UpperCAmelCase    (			a_	,     a_	,     a_	,     a_		)	->			np.ndarray:







				"""simple docstring"""



				__A         =				weight_matrix(_UpperCAmelCase	,     _UpperCAmelCase	,     _UpperCAmelCase		)
				__A         =				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_		)	->			np.ndarray:







				"""simple docstring"""



				__A         =				np.zeros(len(_UpperCAmelCase		)		)  # Initialize array of predictions
				for i, item in enumerate(_UpperCAmelCase		):
								__A         =				item @ local_weight(_UpperCAmelCase	,     _UpperCAmelCase	,     _UpperCAmelCase	,     _UpperCAmelCase		)

				return y_pred


def 		UpperCAmelCase    (			a_	,     a_	,     a_		)	->			tuple[np.ndarray, np.ndarray, np.ndarray]:







				"""simple docstring"""



				import seaborn as sns

				__A         =				sns.load_dataset(_UpperCAmelCase		)
				__A         =				np.array(data[x_name]		)
				__A         =				np.array(data[y_name]		)

				__A         =				np.ones(len(_UpperCAmelCase		)		)

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

				return x_train, x_data, y_data


def 		UpperCAmelCase    (			a_	,     a_	,     a_	,     a_	,     a_	,     a_	,     )	->			None:







				"""simple docstring"""



				__A         =				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
					SCREAMING_SNAKE_CASE				,					SCREAMING_SNAKE_CASE				,					SCREAMING_SNAKE_CASE							:List[Any]											=       load_data('tips', 'total_bill', 'tip')
					SCREAMING_SNAKE_CASE							:List[Any]											=       local_weight_regression(training_data_x, tip, 5)
					plot_preds(training_data_x, predictions, total_bill, tip, 'total_bill', 'tip')


def 		UpperCAmelCase    (			a_		)	->			int:







				"""simple docstring"""



				__A         =				str(a_		).strip()
				if not oct_string:
								raise ValueError("Empty string was passed to the function"		)
				__A         =				oct_string[0] == "-"
				if is_negative:
								__A         =				oct_string[1:]
				if not oct_string.isdigit() or not all(0 <= int(a_		) <= 7 for char in oct_string		):
								raise ValueError("Non-octal value was passed to the function"		)
				__A         =				0
				for char in oct_string:
								__A         =				8 * decimal_number + int(a_		)
				if is_negative:
								__A         =				-decimal_number
				return decimal_number


if __name__ == "__main__":
					from doctest import testmod

					testmod()
