






import matplotlib.pyplot as plt
import numpy as np




def   lowercase__   (  __snake_case					:							List[str]  , __snake_case					:							Union[str, Any]  , __snake_case					:							Any						):


					'''simple docstring'''


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

					return weights




def   lowercase__   (  __snake_case					:							Dict  , __snake_case					:							List[str]  , __snake_case					:							Any  , __snake_case					:							Dict						):


					'''simple docstring'''


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

					return weight




def   lowercase__   (  __snake_case					:							Tuple  , __snake_case					:							str  , __snake_case					:							Union[str, Any]						):


					'''simple docstring'''


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

					return y_pred




def   lowercase__   (  __snake_case					:							Tuple  , __snake_case					:							Any  , __snake_case					:							List[Any]						):


					'''simple docstring'''


					import seaborn as sns

					UpperCAmelCase_					:   List[str]   =		sns.load_dataset(_UpperCAmelCase						)
					UpperCAmelCase_					:   Tuple   =		np.array(data[x_name]						)
					UpperCAmelCase_					:   Dict   =		np.array(data[y_name]						)

					UpperCAmelCase_					:   Union[str, Any]   =		np.ones(len(_UpperCAmelCase						)						)

					# pairing elements of one and x_data
					UpperCAmelCase_					:   Union[str, Any]   =		np.column_stack((one, x_data)						)

					return x_train, x_data, y_data




def   lowercase__   (  __snake_case					:							Dict  , __snake_case					:							Tuple  , __snake_case					:							Union[str, Any]  , __snake_case					:							Tuple  , __snake_case					:							Optional[int]  , __snake_case					:							Optional[Any]  , ):


					'''simple docstring'''


					UpperCAmelCase_					:   Tuple   =		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										=		load_data('tips', 'total_bill', 'tip')
		__UpperCAmelCase										=		local_weight_regression(training_data_x, tip, 5)
		plot_preds(training_data_x, predictions, total_bill, tip, 'total_bill', 'tip')














from __future__ import annotations




def   lowercase__   (  __snake_case					:							Any  , __snake_case					:							int						):


					'''simple docstring'''


					UpperCAmelCase_					:   Optional[int]   =		0
					UpperCAmelCase_					:   Optional[int]   =		len(__snake_case						) - 1
					while left <= right:
										UpperCAmelCase_					:   Optional[Any]   =		(left + right) // 2
										if left == right:
															if sorted_list[middle] < item:
																				UpperCAmelCase_					:   List[Any]   =		middle + 1
															break
										elif sorted_list[middle] < item:
															UpperCAmelCase_					:   Union[str, Any]   =		middle + 1
										else:
															UpperCAmelCase_					:   Tuple   =		middle - 1
					sorted_list.insert(__snake_case  , __snake_case						)
					return sorted_list




def   lowercase__   (  __snake_case					:							Union[str, Any]  , __snake_case					:							int						):


					'''simple docstring'''


					UpperCAmelCase_					:   str   =		[]
					while left and right:
										if left[0][0] < right[0][0]:
															result.append(left.pop(0						)						)
										else:
															result.append(right.pop(0						)						)
					return result + left + right




def   lowercase__   (  __snake_case					:							Dict						):


					'''simple docstring'''


					UpperCAmelCase_					:   str   =		len(__snake_case						)
					if length <= 1:
										return list_ad
					UpperCAmelCase_					:   List[Any]   =		length // 2
					return merge(sortlist_ad(list_ad[:middle]						)  , sortlist_ad(list_ad[middle:]						)						)




def   lowercase__   (  __snake_case					:							list[int]						):


					'''simple docstring'''


					if len(__snake_case						) <= 1:
										return collection
					UpperCAmelCase_					:   Any   =		[]
					UpperCAmelCase_					:   Union[str, Any]   =		False
					for i in range(0  , len(__snake_case						)  , 2						):
										if i == len(__snake_case						) - 1:
															UpperCAmelCase_					:   Tuple   =		True
										else:
															if collection[i] < collection[i + 1]:
																				two_paired_list.append([collection[i], collection[i + 1]]						)
															else:
																				two_paired_list.append([collection[i + 1], collection[i]]						)
					UpperCAmelCase_					:   Union[str, Any]   =		sortlist_ad(__snake_case						)
					UpperCAmelCase_					:   Any   =		[i[0] for i in sorted_list_ad]
					result.append(sorted_list_ad[-1][1]						)
					if has_last_odd_item:
										UpperCAmelCase_					:   Union[str, Any]   =		collection[-1]
										UpperCAmelCase_					:   List[Any]   =		binary_search_insertion(__snake_case  , __snake_case						)
					UpperCAmelCase_					:   Tuple   =		False
					for i in range(len(__snake_case						) - 1						):
										if result[i] == collection[-1] and has_last_odd_item:
															UpperCAmelCase_					:   List[Any]   =		True
										UpperCAmelCase_					:   Optional[int]   =		sorted_list_ad[i][1]
										# If last_odd_item is inserted before the item's index,
										# you should forward index one more.
										if is_last_odd_item_inserted_before_this_index:
															UpperCAmelCase_					:   List[str]   =		result[: i + 2] + binary_search_insertion(result[i + 2 :]  , __snake_case						)
										else:
															UpperCAmelCase_					:   List[Any]   =		result[: i + 1] + binary_search_insertion(result[i + 1 :]  , __snake_case						)

					return result


if __name__ == "__main__":
		__UpperCAmelCase										=		input('Enter numbers separated by a comma:\n').strip()
		__UpperCAmelCase										=		[int(item) for item in user_input.split(',')]
		print(merge_insertion_sort(unsorted))






