



'''simple docstring'''







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE     ):
		return int(SCREAMING_SNAKE_CASE     ) if x - int(SCREAMING_SNAKE_CASE     ) >= 0 else int(SCREAMING_SNAKE_CASE     ) - 1


if __name__ == "__main__":
							import doctest

							doctest.testmod()





'''simple docstring'''







import matplotlib.pyplot as plt
import numpy as np







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

		return weights







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:int										=      weight_matrix(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     )
		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  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:int										=      np.zeros(len(SCREAMING_SNAKE_CASE     )     )  # Initialize array of predictions
		for i, item in enumerate(SCREAMING_SNAKE_CASE     ):
				SCREAMING_SNAKE_CASE_						:Dict										=      item @ local_weight(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     )

		return y_pred







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		import seaborn as sns

		SCREAMING_SNAKE_CASE_						:Union[str, Any]										=      sns.load_dataset(SCREAMING_SNAKE_CASE     )
		SCREAMING_SNAKE_CASE_						:Tuple										=      np.array(data[x_name]     )
		SCREAMING_SNAKE_CASE_						:Optional[int]										=      np.array(data[y_name]     )

		SCREAMING_SNAKE_CASE_						:str										=      np.ones(len(SCREAMING_SNAKE_CASE     )     )

		# pairing elements of one and x_data
		SCREAMING_SNAKE_CASE_						:Optional[int]										=      np.column_stack((one, x_data)     )

		return x_train, x_data, y_data







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		):
		SCREAMING_SNAKE_CASE_						:Tuple										=      np.sort(SCREAMING_SNAKE_CASE ,		axis=0     )
		plt.scatter(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		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(SCREAMING_SNAKE_CASE     )
		plt.ylabel(SCREAMING_SNAKE_CASE     )
		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__     : str				=   load_data("""tips""", """total_bill""", """tip""")
							SCREAMING_SNAKE_CASE__     : str				=   local_weight_regression(training_data_x, tip, 5)
							plot_preds(training_data_x, predictions, total_bill, tip, """total_bill""", """tip""")
