


"""simple docstring"""






import matplotlib.pyplot as plt
import numpy as np


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

				return weights


def __lowercase  (   lowerCamelCase_	:   np.ndarray    ,       lowerCamelCase_	:   np.ndarray    ,       lowerCamelCase_	:   np.ndarray    ,       lowerCamelCase_	:   float	):
				SCREAMING_SNAKE_CASE__  				=					weight_matrix(lowerCamelCase_    ,       lowerCamelCase_    ,       lowerCamelCase_	)
				SCREAMING_SNAKE_CASE__  				=					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	):
				SCREAMING_SNAKE_CASE__  				=					np.zeros(len(lowerCamelCase_	)	)  # Initialize array of predictions
				for i, item in enumerate(lowerCamelCase_	):
								SCREAMING_SNAKE_CASE__  				=					item @ local_weight(lowerCamelCase_    ,       lowerCamelCase_    ,       lowerCamelCase_    ,       lowerCamelCase_	)

				return y_pred


def __lowercase  (   lowerCamelCase_	:   str    ,       lowerCamelCase_	:   str    ,       lowerCamelCase_	:   str	):
				import seaborn as sns

				SCREAMING_SNAKE_CASE__  				=					sns.load_dataset(lowerCamelCase_	)
				SCREAMING_SNAKE_CASE__  				=					np.array(data[x_name]	)
				SCREAMING_SNAKE_CASE__  				=					np.array(data[y_name]	)

				SCREAMING_SNAKE_CASE__  				=					np.ones(len(lowerCamelCase_	)	)

				# pairing elements of one and x_data
				SCREAMING_SNAKE_CASE__  				=					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    ,       ):
				SCREAMING_SNAKE_CASE__  				=					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  ,  _lowerCamelCase  ,  _lowerCamelCase  =	load_data('tips', 'total_bill', 'tip')
	_lowerCamelCase  =	local_weight_regression(training_data_x, tip, 5)
	plot_preds(training_data_x, predictions, total_bill, tip, 'total_bill', 'tip')




"""simple docstring"""






class       lowerCamelCase_		:





				"""simple docstring"""







				class       lowerCamelCase_		:





								"""simple docstring"""







								_lowerCAmelCase   :   Dict   				=       "_prev", "_data", "_next"



								def __init__(    self							,		UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__  ):
												SCREAMING_SNAKE_CASE__  				=					link_p
												SCREAMING_SNAKE_CASE__  				=					element
												SCREAMING_SNAKE_CASE__  				=					link_n






								def 	lowerCAmelCase__		(    self  ):
												return (
												    f''' Prev -> {self._prev is not None}, Next -> {self._next is not None}'''
												)



				def __init__(    self  ):
								SCREAMING_SNAKE_CASE__  				=					self._Node(UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__  )
								SCREAMING_SNAKE_CASE__  				=					self._Node(UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__  )
								SCREAMING_SNAKE_CASE__  				=					self._trailer
								SCREAMING_SNAKE_CASE__  				=					self._header
								SCREAMING_SNAKE_CASE__  				=					0



				def __len__(    self  ):
								return self._size



				def 	lowerCAmelCase__		(    self  ):
								return self.__len__() == 0



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__  ):
								# Create new_node by setting it's prev.link -> header
								# setting it's next.link -> trailer
								SCREAMING_SNAKE_CASE__  				=					self._Node(UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__  )
								SCREAMING_SNAKE_CASE__  				=					new_node
								SCREAMING_SNAKE_CASE__  				=					new_node
								self._size += 1
								return self






				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								SCREAMING_SNAKE_CASE__  				=					node._prev
								SCREAMING_SNAKE_CASE__  				=					node._next

								SCREAMING_SNAKE_CASE__  				=					successor
								SCREAMING_SNAKE_CASE__  				=					predecessor
								self._size -= 1
								SCREAMING_SNAKE_CASE__  				=					node._data
								SCREAMING_SNAKE_CASE__  				=					SCREAMING_SNAKE_CASE__  				=					SCREAMING_SNAKE_CASE__  				=					None
								del node
								return temp


class       lowerCamelCase_		(      _DoublyLinkedBase ):





				"""simple docstring"""







				def 	lowerCAmelCase__		(    self  ):
								if self.is_empty():
												raise Exception("List is empty"  )
								return self._header._next._data



				def 	lowerCAmelCase__		(    self  ):
								if self.is_empty():
												raise Exception("List is empty"  )
								return self._trailer._prev._data



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								return self._insert(self._header							,		UpperCAmelCase__							,		self._header._next  )



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								return self._insert(self._trailer._prev							,		UpperCAmelCase__							,		self._trailer  )



				def 	lowerCAmelCase__		(    self  ):
								if self.is_empty():
												raise IndexError("remove_first from empty list"  )
								return self._delete(self._header._next  )






				def 	lowerCAmelCase__		(    self  ):
								if self.is_empty():
												raise IndexError("remove_first from empty list"  )
								return self._delete(self._trailer._prev  )
