




import matplotlib.pyplot as plt
import numpy as np

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

     return weights

def       __lowerCamelCase							(     __UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase)    ->  np.ndarray:
     a											=   weight_matrix(__UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase)
     a											=   np.linalg.inv(x_train.T @ weight_mat @ x_train) @ (
         x_train.T @ weight_mat @ y_train.T
     )

     return weight

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

     return y_pred

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

     a											=   sns.load_dataset(__UpperCamelCase)
     a											=   np.array(data[x_name])
     a											=   np.array(data[y_name])

     a											=   np.ones(len(__UpperCamelCase))

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

     return x_train, x_data, y_data

def       __lowerCamelCase							(     __UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase	,      )    ->  None:
     a											=   np.sort(__UpperCamelCase	,      axis=0)
     plt.scatter(__UpperCamelCase	,      __UpperCamelCase	,      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(__UpperCamelCase)
     plt.ylabel(__UpperCamelCase)
     plt.show()


if __name__ == "__main__":
   import doctest

   doctest.testmod()

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







from __future__ import annotations

def       SCREAMING_SNAKE_CASE							(     __UpperCamelCase)    ->  int | None:
     for r in range(1	,      __UpperCamelCase):
          a											=   []
          for x in range(n - 1):
               a											=   pow(__UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase)
               if val in li:
                    break
               li.append(__UpperCamelCase)
          else:
               return r
     return None


if __name__ == "__main__":
   lowercase__   :    Tuple 					=      int(input("Enter a prime number q: "))
   lowercase__   :    List[Any] 					=      find_primitive(q)
   if a is None:
      print(F'Cannot find the primitive for the value: {a!r}')
   else:
      lowercase__   :    Any 					=      int(input("Enter private key of A: "))
      lowercase__   :    Optional[int] 					=      pow(a, a_private, q)
      lowercase__   :    Optional[Any] 					=      int(input("Enter private key of B: "))
      lowercase__   :    Any 					=      pow(a, b_private, q)

      lowercase__   :    Optional[Any] 					=      pow(b_public, a_private, q)
      lowercase__   :    List[str] 					=      pow(a_public, b_private, q)

      print("The key value generated by A is: ", a_secret)
      print("The key value generated by B is: ", b_secret)

