





'''simple docstring'''







import matplotlib.pyplot as plt
import numpy as np

def 		SCREAMING_SNAKE_CASE      (					lowerCAmelCase__     :	np.ndarray       ,  lowerCAmelCase__     :	np.ndarray       ,  lowerCAmelCase__     :	float)			->						np.ndarray:

     '''simple docstring'''




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

     return weights

def 		SCREAMING_SNAKE_CASE      (					lowerCAmelCase__     :	np.ndarray       ,  lowerCAmelCase__     :	np.ndarray       ,  lowerCAmelCase__     :	np.ndarray       ,  lowerCAmelCase__     :	float)			->						np.ndarray:

     '''simple docstring'''




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

     return weight

def 		SCREAMING_SNAKE_CASE      (					lowerCAmelCase__     :	np.ndarray       ,  lowerCAmelCase__     :	np.ndarray       ,  lowerCAmelCase__     :	float)			->						np.ndarray:

     '''simple docstring'''




     _lowercase							:      List[Any]  						=							np.zeros(len(lowerCAmelCase__))  # Initialize array of predictions
     for i, item in enumerate(lowerCAmelCase__):
          _lowercase							:      Optional[int]  						=							item @ local_weight(lowerCAmelCase__       ,  lowerCAmelCase__       ,  lowerCAmelCase__       ,  lowerCAmelCase__)

     return y_pred

def 		SCREAMING_SNAKE_CASE      (					lowerCAmelCase__     :	str       ,  lowerCAmelCase__     :	str       ,  lowerCAmelCase__     :	str)			->						tuple[np.ndarray, np.ndarray, np.ndarray]:

     '''simple docstring'''




     import seaborn as sns

     _lowercase							:      Tuple  						=							sns.load_dataset(lowerCAmelCase__)
     _lowercase							:      List[Any]  						=							np.array(data[x_name])
     _lowercase							:      Optional[int]  						=							np.array(data[y_name])

     _lowercase							:      Any  						=							np.ones(len(lowerCAmelCase__))

     # pairing elements of one and x_data
     _lowercase							:      int  						=							np.column_stack((one, x_data))

     return x_train, x_data, y_data

def 		SCREAMING_SNAKE_CASE      (					lowerCAmelCase__     :	np.ndarray       ,  lowerCAmelCase__     :	np.ndarray       ,  lowerCAmelCase__     :	np.ndarray       ,  lowerCAmelCase__     :	np.ndarray       ,  lowerCAmelCase__     :	str       ,  lowerCAmelCase__     :	str       ,  )			->						None:

     '''simple docstring'''




     _lowercase							:      Optional[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
    A    ,       A    ,       A						    =							load_data('''tips''', '''total_bill''', '''tip''')
    A						    =							local_weight_regression(training_data_x, tip, 5)
    plot_preds(training_data_x, predictions, total_bill, tip, '''total_bill''', '''tip''')






'''simple docstring'''







def 		SCREAMING_SNAKE_CASE      (					lowerCAmelCase__     :	str)			->						str:

     '''simple docstring'''




     return " ".join(sorted(set(sentence.split())))


if __name__ == "__main__":
    import doctest

    doctest.testmod()