




'''simple docstring'''
import matplotlib.pyplot as plt
import numpy as np





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

			return weights





def  lowerCamelCase(       SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )		->		np.ndarray:
			A_       		=   weight_matrix(SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )
			A_       		=   np.linalg.inv(x_train.T @ weight_mat @ x_train    ) @ (
			    x_train.T @ weight_mat @ y_train.T
			)

			return weight





def  lowerCamelCase(       SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )		->		np.ndarray:
			A_       		=   np.zeros(len(SCREAMING_SNAKE_CASE_    )    )  # Initialize array of predictions
			for i, item in enumerate(SCREAMING_SNAKE_CASE_    ):
						A_       		=   item @ local_weight(SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )

			return y_pred





def  lowerCamelCase(       SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )		->		tuple[np.ndarray, np.ndarray, np.ndarray]:
			import seaborn as sns

			A_       		=   sns.load_dataset(SCREAMING_SNAKE_CASE_    )
			A_       		=   np.array(data[x_name]    )
			A_       		=   np.array(data[y_name]    )

			A_       		=   np.ones(len(SCREAMING_SNAKE_CASE_    )    )

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

			return x_train, x_data, y_data





def  lowerCamelCase(       SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,)		->		None:
			A_       		=   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 =	load_data("tips", "total_bill", "tip")
							_SCREAMING_SNAKE_CASE =	local_weight_regression(training_data_x, tip, 5)
							plot_preds(training_data_x, predictions, total_bill, tip, "total_bill", "tip")










'''simple docstring'''
def  lowerCamelCase(       SCREAMING_SNAKE_CASE_    )		->		list:
			A_       		=   [True for i in range(n + 1    )]
			A_       		=   [i - 1 for i in range(n + 1    )]
			A_       		=   []
			for i in range(2					,n + 1    ):
						if is_prime[i]:
									primes.append(SCREAMING_SNAKE_CASE_    )
						for j in range(0					,len(SCREAMING_SNAKE_CASE_    )    ):
									if i * primes[j] >= n:
												break
									A_       		=   False

									if i % primes[j] == 0:
												A_       		=   totients[i] * primes[j]
												break

									A_       		=   totients[i] * (primes[j] - 1)

			return totients


if __name__ == "__main__":
							import doctest

							doctest.testmod()




