





import matplotlib.pyplot as plt
import numpy as np
def  __UpperCamelCase    (						snake_case							,			snake_case							,			snake_case      )    ->		Optional[int]:


   '''simple docstring'''







   __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  __UpperCamelCase    (						snake_case							,			snake_case							,			snake_case							,			snake_case      )    ->		Union[str, Any]:


   '''simple docstring'''







   __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  __UpperCamelCase    (						snake_case							,			snake_case							,			snake_case      )    ->		Optional[int]:


   '''simple docstring'''







   __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  __UpperCamelCase    (						snake_case							,			snake_case							,			snake_case      )    ->		Optional[int]:


   '''simple docstring'''







   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  __UpperCamelCase    (						snake_case							,			snake_case							,			snake_case							,			snake_case							,			snake_case							,			snake_case							,			)    ->		Dict:


   '''simple docstring'''







   __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
    _UpperCamelCase       ,    _UpperCamelCase       ,    _UpperCamelCase       :				Union[str, Any]           =			load_data("""tips""", """total_bill""", """tip""")
    _UpperCamelCase       :				Tuple           =			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

import math
import random


def   __lowerCAmelCase(		__UpperCAmelCase  ,__UpperCAmelCase  ,__UpperCAmelCase      ):






	"""simple docstring"""





	_lowercase			:     Optional[int]      					=				d * e - 1
	_lowercase			:     int      					=				0
	_lowercase			:     Union[str, Any]      					=				0
	while p == 0:
		_lowercase			:     int      					=				random.randint(2  ,n - 1      )
		_lowercase			:     str      					=				k
		while True:
			if t % 2 == 0:
				_lowercase			:     List[Any]      					=				t // 2
				_lowercase			:     int      					=				(g**t) % n
				_lowercase			:     Tuple      					=				math.gcd(x - 1  ,__UpperCAmelCase      )
				if x > 1 and y > 1:
					_lowercase			:     List[str]      					=				y
					_lowercase			:     str      					=				n // y
					break  # find the correct factors
			else:
				break  # t is not divisible by 2, break and choose another g
	return sorted([p, q]      )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



