"""simple docstring"""







import matplotlib.pyplot as plt
import numpy as np




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				str  ,       _SCREAMING_SNAKE_CASE				:				Tuple  ,       _SCREAMING_SNAKE_CASE				:				Dict						)    ->     Union[str, Any]:







     '''simple docstring'''


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

     return weights




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				Dict  ,       _SCREAMING_SNAKE_CASE				:				List[str]  ,       _SCREAMING_SNAKE_CASE				:				Optional[int]  ,       _SCREAMING_SNAKE_CASE				:				Any						)    ->     int:







     '''simple docstring'''


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

     return weight




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				Optional[int]  ,       _SCREAMING_SNAKE_CASE				:				str  ,       _SCREAMING_SNAKE_CASE				:				Dict						)    ->     Dict:







     '''simple docstring'''


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

     return y_pred




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				Tuple  ,       _SCREAMING_SNAKE_CASE				:				int  ,       _SCREAMING_SNAKE_CASE				:				Dict						)    ->     Union[str, Any]:







     '''simple docstring'''


     import seaborn as sns

     __A					:					int								=		sns.load_dataset(lowerCAmelCase_						)
     __A					:					List[str]								=		np.array(data[x_name]						)
     __A					:					Any								=		np.array(data[y_name]						)

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

     # pairing elements of one and x_data
     __A					:					List[Any]								=		np.column_stack((one, x_data)						)

     return x_train, x_data, y_data




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				Tuple  ,       _SCREAMING_SNAKE_CASE				:				Dict  ,       _SCREAMING_SNAKE_CASE				:				List[str]  ,       _SCREAMING_SNAKE_CASE				:				Union[str, Any]  ,       _SCREAMING_SNAKE_CASE				:				str  ,       _SCREAMING_SNAKE_CASE				:				Union[str, Any]  ,       )    ->     str:







     '''simple docstring'''


     __A					:					Union[str, 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
       lowerCamelCase      : List[Any]       =load_data('''tips''', '''total_bill''', '''tip''')
       lowerCamelCase      : int       =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




def  _a     (				lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_						):





      """simple docstring"""



      if counter == 0 or capacity == 0:
            return 0

      # If weight of the nth item is more than Knapsack of capacity,
      #   then this item cannot be included in the optimal solution,
      # else return the maximum of two cases:
      #   (1) nth item included
      #   (2) not included
      if weights[counter - 1] > capacity:
            return knapsack(lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   counter - 1						)
      else:
            _snake_case		:						List[str]         =  capacity - weights[counter - 1]
            _snake_case		:						Tuple         =  values[counter - 1] + knapsack(
                lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   counter - 1						)
            _snake_case		:						Any         =  knapsack(lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   counter - 1						)
            return max(lowerCAmelCase_      ,   lowerCAmelCase_						)


if __name__ == "__main__":
   import doctest

   doctest.testmod()


