
"""simple docstring"""






import matplotlib.pyplot as plt
import numpy as np






def 		_snake_case			(      lowercase__						:    np.ndarray ,	lowercase__						:    np.ndarray ,	lowercase__						:    float						)    ->							np.ndarray:


			'''simple docstring'''





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

			return weights






def 		_snake_case			(      lowercase__						:    np.ndarray ,	lowercase__						:    np.ndarray ,	lowercase__						:    np.ndarray ,	lowercase__						:    float						)    ->							np.ndarray:


			'''simple docstring'''





			lowerCAmelCase_       :int     	=    weight_matrix(lowercase__ ,	lowercase__ ,	lowercase__						)
			lowerCAmelCase_       :Union[str, Any]     	=    np.linalg.inv(x_train.T @ weight_mat @ x_train						) @ (
			    x_train.T @ weight_mat @ y_train.T
			)

			return weight






def 		_snake_case			(      lowercase__						:    np.ndarray ,	lowercase__						:    np.ndarray ,	lowercase__						:    float						)    ->							np.ndarray:


			'''simple docstring'''





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

			return y_pred






def 		_snake_case			(      lowercase__						:    str ,	lowercase__						:    str ,	lowercase__						:    str						)    ->							tuple[np.ndarray, np.ndarray, np.ndarray]:


			'''simple docstring'''





			import seaborn as sns

			lowerCAmelCase_       :Dict     	=    sns.load_dataset(lowercase__						)
			lowerCAmelCase_       :Union[str, Any]     	=    np.array(data[x_name]						)
			lowerCAmelCase_       :Union[str, Any]     	=    np.array(data[y_name]						)

			lowerCAmelCase_       :int     	=    np.ones(len(lowercase__						)						)

			# pairing elements of one and x_data
			lowerCAmelCase_       :Union[str, Any]     	=    np.column_stack((one, x_data)						)

			return x_train, x_data, y_data






def 		_snake_case			(      lowercase__						:    np.ndarray ,	lowercase__						:    np.ndarray ,	lowercase__						:    np.ndarray ,	lowercase__						:    np.ndarray ,	lowercase__						:    str ,	lowercase__						:    str ,	)    ->							None:


			'''simple docstring'''





			lowerCAmelCase_       :Union[str, Any]     	=    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
				__UpperCAmelCase					,					__UpperCAmelCase					,					__UpperCAmelCase 					=    load_data('tips', 'total_bill', 'tip')
				__UpperCAmelCase 					=    local_weight_regression(training_data_x, tip, 5)
				plot_preds(training_data_x, predictions, total_bill, tip, 'total_bill', 'tip')








"""simple docstring"""






from __future__ import annotations






def 		_snake_case			(      lowercase__						:    list[int | float]						)    ->							int | float:


			'''simple docstring'''





			if len(lowercase__						) == 0:
						raise ValueError("""find_min() arg is an empty sequence"""						)
			lowerCAmelCase_       :Optional[int]     	=    nums[0]
			for num in nums:
						lowerCAmelCase_       :Optional[Any]     	=    min(lowercase__ ,	lowercase__						)
			return min_num


if __name__ == "__main__":
				import doctest

				doctest.testmod(verbose=True)






