






"""simple docstring"""



import matplotlib.pyplot as plt
import numpy as np


def      SCREAMING_SNAKE_CASE__    (   snake_case    :      Any       , snake_case    :      Union[str, Any]       , snake_case    :      Optional[int]							)->						Dict:






     '''simple docstring'''



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

     return weights


def      SCREAMING_SNAKE_CASE__    (   snake_case    :      Tuple       , snake_case    :      Union[str, Any]       , snake_case    :      Union[str, Any]       , snake_case    :      List[str]							)->						Any:






     '''simple docstring'''



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

     return weight


def      SCREAMING_SNAKE_CASE__    (   snake_case    :      Any       , snake_case    :      Union[str, Any]       , snake_case    :      int							)->						str:






     '''simple docstring'''



     UpperCAmelCase__		:  Tuple				=				np.zeros(len(lowerCAmelCase_							)							)  # Initialize array of predictions
     for i, item in enumerate(lowerCAmelCase_							):
          UpperCAmelCase__		:  List[Any]				=				item @ local_weight(lowerCAmelCase_       , lowerCAmelCase_       , lowerCAmelCase_       , lowerCAmelCase_							)

     return y_pred


def      SCREAMING_SNAKE_CASE__    (   snake_case    :      Any       , snake_case    :      Any       , snake_case    :      int							)->						List[Any]:






     '''simple docstring'''



     import seaborn as sns

     UpperCAmelCase__		:  Any				=				sns.load_dataset(lowerCAmelCase_							)
     UpperCAmelCase__		:  int				=				np.array(data[x_name]							)
     UpperCAmelCase__		:  Optional[Any]				=				np.array(data[y_name]							)

     UpperCAmelCase__		:  Dict				=				np.ones(len(lowerCAmelCase_							)							)

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

     return x_train, x_data, y_data


def      SCREAMING_SNAKE_CASE__    (   snake_case    :      Optional[Any]       , snake_case    :      Dict       , snake_case    :      str       , snake_case    :      List[Any]       , snake_case    :      Tuple       , snake_case    :      List[Any]       , )->						Any:






     '''simple docstring'''



     UpperCAmelCase__		:  Dict				=				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
 _lowerCAmelCase     :     Optional[Any]            =	load_data("""tips""", """total_bill""", """tip""")
 _lowerCAmelCase     :     Union[str, Any]            =	local_weight_regression(training_data_x, tip, 5)
 plot_preds(training_data_x, predictions, total_bill, tip, """total_bill""", """tip""")




'''simple docstring'''

from itertools import combinations, product







def __A  (    lowerCAmelCase_ ,       lowerCAmelCase_ ,       lowerCAmelCase_ ,       lowerCAmelCase_       ):
     if xa == ya == 0 or xa == ya == 0:
          return False
     _UpperCAmelCase					:  Any         =    xa * xa + ya * ya
     _UpperCAmelCase					:  Any         =    xa * xa + ya * ya
     _UpperCAmelCase					:  Tuple         =    (xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
     return (
         a_square + b_square == c_square
         or a_square + c_square == b_square
         or b_square + c_square == a_square
     )







def __A  (    lowerCAmelCase_ = 50       ):
     return sum(
         1
         for pta, pta in combinations(product(range(limit + 1       ) ,       repeat=2       ) ,       2       )
         if is_right(*lowerCAmelCase_ ,       *lowerCAmelCase_       )       )


if __name__ == "__main__":
   print(F"{solution() = }")


