



import matplotlib.pyplot as plt
import numpy as np



def  lowercase    (				SCREAMING_SNAKE_CASE__    :		np.ndarray			,    SCREAMING_SNAKE_CASE__    :		np.ndarray			,    SCREAMING_SNAKE_CASE__    :		float			)					->       np.ndarray:
 _snake_case      :					Union[str, Any]					=   len(SCREAMING_SNAKE_CASE__			)  # Number of training samples
 _snake_case      :					Dict					=   np.eye(SCREAMING_SNAKE_CASE__			)  # Initialize weights as identity matrix
 for j in range(SCREAMING_SNAKE_CASE__			):
  _snake_case      :					List[Any]					=   point - x_train[j]
  _snake_case      :					Optional[int]					=   np.exp(diff @ diff.T / (-2.0 * tau**2)			)

 return weights



def  lowercase    (				SCREAMING_SNAKE_CASE__    :		np.ndarray			,    SCREAMING_SNAKE_CASE__    :		np.ndarray			,    SCREAMING_SNAKE_CASE__    :		np.ndarray			,    SCREAMING_SNAKE_CASE__    :		float			)					->       np.ndarray:
 _snake_case      :					Tuple					=   weight_matrix(SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__			)
 _snake_case      :					Any					=   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__    :		np.ndarray			,    SCREAMING_SNAKE_CASE__    :		np.ndarray			,    SCREAMING_SNAKE_CASE__    :		float			)					->       np.ndarray:
 _snake_case      :					Any					=   np.zeros(len(SCREAMING_SNAKE_CASE__			)			)  # Initialize array of predictions
 for i, item in enumerate(SCREAMING_SNAKE_CASE__			):
  _snake_case      :					List[str]					=   item @ local_weight(SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__			)

 return y_pred



def  lowercase    (				SCREAMING_SNAKE_CASE__    :		str			,    SCREAMING_SNAKE_CASE__    :		str			,    SCREAMING_SNAKE_CASE__    :		str			)					->       tuple[np.ndarray, np.ndarray, np.ndarray]:
 import seaborn as sns

 _snake_case      :					Optional[int]					=   sns.load_dataset(SCREAMING_SNAKE_CASE__			)
 _snake_case      :					List[str]					=   np.array(data[x_name]			)
 _snake_case      :					Any					=   np.array(data[y_name]			)

 _snake_case      :					str					=   np.ones(len(SCREAMING_SNAKE_CASE__			)			)

 # pairing elements of one and x_data
 _snake_case      :					Any					=   np.column_stack((one, x_data)			)

 return x_train, x_data, y_data



def  lowercase    (				SCREAMING_SNAKE_CASE__    :		np.ndarray			,    SCREAMING_SNAKE_CASE__    :		np.ndarray			,    SCREAMING_SNAKE_CASE__    :		np.ndarray			,    SCREAMING_SNAKE_CASE__    :		np.ndarray			,    SCREAMING_SNAKE_CASE__    :		str			,    SCREAMING_SNAKE_CASE__    :		str			,    )					->       None:
 _snake_case      :					Any					=   np.sort(SCREAMING_SNAKE_CASE__			,    axis=0			)
 plt.scatter(SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__			,    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(SCREAMING_SNAKE_CASE__			)
 plt.ylabel(SCREAMING_SNAKE_CASE__			)
 plt.show()


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  # Demo with a dataset from the seaborn module
  a__,  a__,  a__      =		load_data("""tips""", """total_bill""", """tip""")
  a__      =		local_weight_regression(training_data_x, tip, 5)
  plot_preds(training_data_x, predictions, total_bill, tip, """total_bill""", """tip""")





def  lowercase    (				SCREAMING_SNAKE_CASE__    :		float			,    SCREAMING_SNAKE_CASE__    :		float			)					->       float:
 _snake_case      :					str					=   float()
 try:
  _snake_case      :					str					=   mass * acceleration
 except Exception:
  return -0.0
 return force


if __name__ == "__main__":
  import doctest

  # run doctest
  doctest.testmod()

  # demo
  a__      =		12.5
  a__      =		10
  a__      =		newtons_second_law_of_motion(mass, acceleration)
  print("""The force is """, force, """N""")
