





import matplotlib.pyplot as plt
import numpy as np


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

    return weights


def        __snake_case       (						lowerCAmelCase_   ,       lowerCAmelCase_   ,       lowerCAmelCase_   ,       lowerCAmelCase_  )							->	np.ndarray:
    SCREAMING_SNAKE_CASE__       							= weight_matrix(lowerCAmelCase_   ,       lowerCAmelCase_   ,       lowerCAmelCase_  )
    SCREAMING_SNAKE_CASE__       							= np.linalg.inv(x_train.T @ weight_mat @ x_train  ) @ (
        x_train.T @ weight_mat @ y_train.T
    )

    return weight


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

    return y_pred


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

    SCREAMING_SNAKE_CASE__       							= sns.load_dataset(lowerCAmelCase_  )
    SCREAMING_SNAKE_CASE__       							= np.array(data[x_name]  )
    SCREAMING_SNAKE_CASE__       							= np.array(data[y_name]  )

    SCREAMING_SNAKE_CASE__       							= np.ones(len(lowerCAmelCase_  )  )

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

    return x_train, x_data, y_data


def        __snake_case       (						lowerCAmelCase_   ,       lowerCAmelCase_   ,       lowerCAmelCase_   ,       lowerCAmelCase_   ,       lowerCAmelCase_   ,       lowerCAmelCase_   ,       )							->	None:
    SCREAMING_SNAKE_CASE__       							= 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				:							str							= 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""")







import numpy as np

_A				:							List[Any]							= [
    ["""a""", """b""", """c""", """d""", """e"""],
    ["""f""", """g""", """h""", """i""", """k"""],
    ["""l""", """m""", """n""", """o""", """p"""],
    ["""q""", """r""", """s""", """t""", """u"""],
    ["""v""", """w""", """x""", """y""", """z"""],
]



class 				__snake_case  :


    '''simple docstring'''







    def __init__(					self    ):





        '''simple docstring'''

        SCREAMING_SNAKE_CASE__       							= np.array(A_    )



    def    lowercase_				(					self      ,							A_    ):





        '''simple docstring'''

        SCREAMING_SNAKE_CASE__							,		SCREAMING_SNAKE_CASE__       							= np.where(letter == self.SQUARE    )
        SCREAMING_SNAKE_CASE__       							= np.concatenate([indexa + 1, indexa + 1]    )
        return indexes



    def    lowercase_				(					self      ,							A_      ,							A_    ):





        '''simple docstring'''

        return self.SQUARE[indexa - 1, indexa - 1]



    def    lowercase_				(					self      ,							A_    ):





        '''simple docstring'''

        SCREAMING_SNAKE_CASE__       							= message.lower()
        SCREAMING_SNAKE_CASE__       							= message.replace('''j'''      ,							'''i'''    )

        SCREAMING_SNAKE_CASE__       							= ''''''
        for letter_index in range(len(A_    )    ):
            if message[letter_index] != " ":
                SCREAMING_SNAKE_CASE__       							= self.letter_to_numbers(message[letter_index]    )
                SCREAMING_SNAKE_CASE__       							= encoded_message + str(numbers[0]    ) + str(numbers[1]    )
            elif message[letter_index] == " ":
                SCREAMING_SNAKE_CASE__       							= encoded_message + ''' '''

        return encoded_message




    def    lowercase_				(					self      ,							A_    ):





        '''simple docstring'''

        SCREAMING_SNAKE_CASE__       							= message.replace(''' '''      ,							'''  '''    )
        SCREAMING_SNAKE_CASE__       							= ''''''
        for numbers_index in range(int(len(A_    ) / 2    )    ):
            if message[numbers_index * 2] != " ":
                SCREAMING_SNAKE_CASE__       							= message[numbers_index * 2]
                SCREAMING_SNAKE_CASE__       							= message[numbers_index * 2 + 1]

                SCREAMING_SNAKE_CASE__       							= self.numbers_to_letter(int(A_    )      ,							int(A_    )    )
                SCREAMING_SNAKE_CASE__       							= decoded_message + letter
            elif message[numbers_index * 2] == " ":
                SCREAMING_SNAKE_CASE__       							= decoded_message + ''' '''

        return decoded_message
