





'''simple docstring'''






import matplotlib.pyplot as plt
import numpy as np





def      lowercase  (  lowerCAmelCase :						np.ndarray   , lowerCAmelCase :						np.ndarray   , lowerCAmelCase :						float):



				"""simple docstring"""


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

				return weights





def      lowercase  (  lowerCAmelCase :						np.ndarray   , lowerCAmelCase :						np.ndarray   , lowerCAmelCase :						np.ndarray   , lowerCAmelCase :						float):



				"""simple docstring"""


				_A :				Tuple				=  weight_matrix(lowerCAmelCase   , lowerCAmelCase   , lowerCAmelCase)
				_A :				Any				=  np.linalg.inv(x_train.T @ weight_mat @ x_train) @ (
				    x_train.T @ weight_mat @ y_train.T
				)

				return weight





def      lowercase  (  lowerCAmelCase :						np.ndarray   , lowerCAmelCase :						np.ndarray   , lowerCAmelCase :						float):



				"""simple docstring"""


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

				return y_pred





def      lowercase  (  lowerCAmelCase :						str   , lowerCAmelCase :						str   , lowerCAmelCase :						str):



				"""simple docstring"""


				import seaborn as sns

				_A :				List[Any]				=  sns.load_dataset(lowerCAmelCase)
				_A :				Tuple				=  np.array(data[x_name])
				_A :				List[Any]				=  np.array(data[y_name])

				_A :				Optional[int]				=  np.ones(len(lowerCAmelCase))

				# pairing elements of one and x_data
				_A :				int				=  np.column_stack((one, x_data))

				return x_train, x_data, y_data





def      lowercase  (  lowerCAmelCase :						np.ndarray   , lowerCAmelCase :						np.ndarray   , lowerCAmelCase :						np.ndarray   , lowerCAmelCase :						np.ndarray   , lowerCAmelCase :						str   , lowerCAmelCase :						str   , ):



				"""simple docstring"""


				_A :				Optional[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
	__UpperCamelCase							,  __UpperCamelCase							,  __UpperCamelCase      :   Dict								=     load_data('''tips''', '''total_bill''', '''tip''')
	__UpperCamelCase      :   Optional[int]								=     local_weight_regression(training_data_x, tip, 5)
	plot_preds(training_data_x, predictions, total_bill, tip, '''total_bill''', '''tip''')







'''simple docstring'''






from .hash_table import HashTable
from .number_theory.prime_numbers import is_prime, next_prime



class  lowerCamelCase__				(						snake_case_						):


	"""simple docstring"""





	def __init__(					self   ,     *UpperCAmelCase__   ,     **UpperCAmelCase__			)       ->				Optional[int]:
					super().__init__(*UpperCAmelCase__   ,     **UpperCAmelCase__			)




	def 				_lowerCamelCase				(					self   ,     UpperCAmelCase__   ,     UpperCAmelCase__			)       ->				Optional[int]:
					_A :				Union[str, Any]				=  (
					    next_prime(value % self.size_table			)
					    if not is_prime(value % self.size_table			)
					    else value % self.size_table
					)  # gt = bigger than
					return next_prime_gt - (data % next_prime_gt)




	def 				_lowerCamelCase				(					self   ,     UpperCAmelCase__   ,     UpperCAmelCase__   ,     UpperCAmelCase__			)       ->				Union[str, Any]:
					return (increment * self.__hash_function_a(UpperCAmelCase__   ,     UpperCAmelCase__			)) % self.size_table




	def 				_lowerCamelCase				(					self   ,     UpperCAmelCase__   ,     UpperCAmelCase__=None			)       ->				List[Any]:
					_A :				Optional[int]				=  1
					_A :				Optional[int]				=  self.hash_function(UpperCAmelCase__			)

					while self.values[new_key] is not None and self.values[new_key] != key:
									_A :				int				=  (
									    self.__hash_double_function(UpperCAmelCase__   ,     UpperCAmelCase__   ,     UpperCAmelCase__			)
									    if self.balanced_factor() >= self.lim_charge
									    else None
									)
									if new_key is None:
													break
									else:
													i += 1

					return new_key
