"""simple docstring"""




import matplotlib.pyplot as plt
import numpy as np



def 				__a       (			_lowercase							, _lowercase							, _lowercase						):







					"""simple docstring"""





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

					return weights



def 				__a       (			_lowercase							, _lowercase							, _lowercase							, _lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   Any  				=					weight_matrix(lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_						)
					lowerCamelCase__		:   Optional[int]  				=					np.linalg.inv(x_train.T @ weight_mat @ x_train						) @ (
					    x_train.T @ weight_mat @ y_train.T
					)

					return weight



def 				__a       (			_lowercase							, _lowercase							, _lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   Tuple  				=					np.zeros(len(lowerCamelCase_						)						)  # Initialize array of predictions
					for i, item in enumerate(lowerCamelCase_						):
										lowerCamelCase__		:   Dict  				=					item @ local_weight(lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_						)

					return y_pred



def 				__a       (			_lowercase							, _lowercase							, _lowercase						):







					"""simple docstring"""





					import seaborn as sns

					lowerCamelCase__		:   int  				=					sns.load_dataset(lowerCamelCase_						)
					lowerCamelCase__		:   Tuple  				=					np.array(data[x_name]						)
					lowerCamelCase__		:   int  				=					np.array(data[y_name]						)

					lowerCamelCase__		:   Tuple  				=					np.ones(len(lowerCamelCase_						)						)

					# pairing elements of one and x_data
					lowerCamelCase__		:   List[Any]  				=					np.column_stack((one, x_data)						)

					return x_train, x_data, y_data



def 				__a       (			_lowercase							, _lowercase							, _lowercase							, _lowercase							, _lowercase							, _lowercase							, ):







					"""simple docstring"""





					lowerCamelCase__		:   Tuple  				=					np.sort(lowerCamelCase_							, axis=0						)
					plt.scatter(lowerCamelCase_							, lowerCamelCase_							, 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(lowerCamelCase_						)
					plt.ylabel(lowerCamelCase_						)
					plt.show()


if __name__ == "__main__":
					import doctest

					doctest.testmod()

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










"""simple docstring"""






def __lowercase  (   lowerCamelCase_	:   list	):
				if not isinstance(lowerCamelCase_    ,       lowerCamelCase_	):
								raise ValueError("Input series is not valid, valid series - [2, 4, 8]"	)
				if len(lowerCamelCase_	) == 0:
								raise ValueError("Input list must be a non empty list"	)
				if len(lowerCamelCase_	) == 1:
								return True
				try:
								SCREAMING_SNAKE_CASE__  				=					series[1] / series[0]
								for index in range(len(lowerCamelCase_	) - 1	):
												if series[index + 1] / series[index] != common_ratio:
																return False
				except ZeroDivisionError:
								return False
				return True


def __lowercase  (   lowerCamelCase_	:   list	):
				if not isinstance(lowerCamelCase_    ,       lowerCamelCase_	):
								raise ValueError("Input series is not valid, valid series - [2, 4, 8]"	)
				if len(lowerCamelCase_	) == 0:
								raise ValueError("Input list must be a non empty list"	)
				SCREAMING_SNAKE_CASE__  				=					1
				for value in series:
								answer *= value
				return pow(lowerCamelCase_    ,       1 / len(lowerCamelCase_	)	)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
