





import matplotlib.pyplot as plt
import numpy as np





def 						__SCREAMING_SNAKE_CASE  (    UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__			)  ->    List[Any]:







			'''simple docstring'''

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

			return weights





def 						__SCREAMING_SNAKE_CASE  (    UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__			)  ->    Tuple:







			'''simple docstring'''

			UpperCAmelCase       		=    weight_matrix(lowercase__      ,      lowercase__      ,      lowercase__			)
			UpperCAmelCase       		=    np.linalg.inv(x_train.T @ weight_mat @ x_train			) @ (
			    x_train.T @ weight_mat @ y_train.T
			)

			return weight





def 						__SCREAMING_SNAKE_CASE  (    UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__			)  ->    Union[str, Any]:







			'''simple docstring'''

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

			return y_pred





def 						__SCREAMING_SNAKE_CASE  (    UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__			)  ->    str:







			'''simple docstring'''

			import seaborn as sns

			UpperCAmelCase       		=    sns.load_dataset(lowercase__			)
			UpperCAmelCase       		=    np.array(data[x_name]			)
			UpperCAmelCase       		=    np.array(data[y_name]			)

			UpperCAmelCase       		=    np.ones(len(lowercase__			)			)

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

			return x_train, x_data, y_data





def 						__SCREAMING_SNAKE_CASE  (    UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__      ,      )  ->    Union[str, Any]:







			'''simple docstring'''

			UpperCAmelCase       		=    np.sort(lowercase__      ,      axis=0			)
			plt.scatter(lowercase__      ,      lowercase__      ,      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(lowercase__			)
			plt.ylabel(lowercase__			)
			plt.show()


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						# Demo with a dataset from the seaborn module
						__A   ,			__A   ,			__A    :   Any          =       load_data("tips", "total_bill", "tip")
						__A    :   Optional[int]          =       local_weight_regression(training_data_x, tip, 5)
						plot_preds(training_data_x, predictions, total_bill, tip, "total_bill", "tip")










def 						__SCREAMING_SNAKE_CASE  (    UpperCamelCase__      ,      UpperCamelCase__      ,      UpperCamelCase__			)  ->    float:







			'''simple docstring'''

			if mass < 0:
						raise ValueError('''The mass of the body cannot be negative'''			)
			if radius <= 0:
						raise ValueError('''The radius is always a positive non zero integer'''			)
			return (mass * (velocity) ** 2) / radius


if __name__ == "__main__":
				import doctest

				doctest.testmod(verbose=True)



