



import matplotlib.pyplot as plt
import numpy as np




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

			return weights




def 						UpperCAmelCase (    _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase     ):
			A				:       List[Any]														=    weight_matrix(_lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase     )
			A				:       List[str]														=    np.linalg.inv(x_train.T @ weight_mat @ x_train     ) @ (
			    x_train.T @ weight_mat @ y_train.T
			)

			return weight




def 						UpperCAmelCase (    _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase     ):
			A				:       str														=    np.zeros(len(_lowerCamelCase     )     )  # Initialize array of predictions
			for i, item in enumerate(_lowerCamelCase     ):
						A				:       int														=    item @ local_weight(_lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase     )

			return y_pred




def 						UpperCAmelCase (    _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase     ):
			import seaborn as sns

			A				:       Union[str, Any]														=    sns.load_dataset(_lowerCamelCase     )
			A				:       List[Any]														=    np.array(data[x_name]     )
			A				:       List[str]														=    np.array(data[y_name]     )

			A				:       Any														=    np.ones(len(_lowerCamelCase     )     )

			# pairing elements of one and x_data
			A				:       Tuple														=    np.column_stack((one, x_data)     )

			return x_train, x_data, y_data




def 						UpperCAmelCase (    _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase			,     ):
			A				:       Any														=    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
							__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""")




from collections.abc import Callable

__SCREAMING_SNAKE_CASE     =	Callable[[float], float]  # type alias for a real -> real function




def 						UpperCAmelCase (    _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase			,     ):
			A				:       int														=    float(_lowerCamelCase     )
			while True:
						try:
									A				:       Optional[int]														=    prev_guess - function(_lowerCamelCase     ) / derivative(_lowerCamelCase     )
						except ZeroDivisionError:
									raise ZeroDivisionError("Could not find root"     ) from None
						if abs(prev_guess - next_guess     ) < 10**-5:
									return next_guess
						A				:       Any														=    next_guess




def 						UpperCAmelCase (    _lowerCamelCase     ):
			return (x**3) - (2 * x) - 5




def 						UpperCAmelCase (    _lowerCamelCase     ):
			return 3 * (x**2) - 2


if __name__ == "__main__":
							print(newton(f, fa, 3))