
"""simple docstring"""





import matplotlib.pyplot as plt
import numpy as np







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

   return weights







def 			__a  (	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						):
   UpperCAmelCase_      :      Optional[Any]      =					weight_matrix(__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						)
   UpperCAmelCase_      :      Optional[int]      =					np.linalg.inv(x_train.T @ weight_mat @ x_train						) @ (
       x_train.T @ weight_mat @ y_train.T
   )

   return weight







def 			__a  (	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						):
   UpperCAmelCase_      :      Optional[Any]      =					np.zeros(len(__lowerCamelCase						)						)  # Initialize array of predictions
   for i, item in enumerate(__lowerCamelCase						):
      UpperCAmelCase_      :      Dict      =					item @ local_weight(__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						)

   return y_pred







def 			__a  (	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						):
   import seaborn as sns

   UpperCAmelCase_      :      List[str]      =					sns.load_dataset(__lowerCamelCase						)
   UpperCAmelCase_      :      List[Any]      =					np.array(data[x_name]						)
   UpperCAmelCase_      :      Union[str, Any]      =					np.array(data[y_name]						)

   UpperCAmelCase_      :      Optional[Any]      =					np.ones(len(__lowerCamelCase						)						)

   # 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 			__a  (	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	):
   UpperCAmelCase_      :      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
    _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')




"""simple docstring"""





from __future__ import annotations

from typing import Any


class A_			:




  '''simple docstring'''







  def __init__(	self       ,     lowercase_       ,     lowercase_						):  # noqa: A002

     """simple docstring"""
     UpperCAmelCase_      :      Optional[Any]      =					item
     UpperCAmelCase_      :      Optional[Any]      =					next




class A_			:




  '''simple docstring'''







  def __init__(	self						):

     """simple docstring"""
     UpperCAmelCase_      :      Node | None      =					None
     UpperCAmelCase_      :      Optional[int]      =					0







  def  UpperCamelCase__      (	self       ,     lowercase_						):

     """simple docstring"""
     UpperCAmelCase_      :      int      =					Node(lowercase_       ,     self.head						)
     self.size += 1







  def  UpperCamelCase__      (	self						):

     """simple docstring"""
     # Switched 'self.is_empty()' to 'self.head is None'
     # because mypy was considering the possibility that 'self.head'
     # can be None in below else part and giving error
     if self.head is None:
        return None
     else:
        UpperCAmelCase_      :      int      =					self.head.item
        UpperCAmelCase_      :      str      =					self.head.next
        self.size -= 1
        return item







  def  UpperCamelCase__      (	self						):

     """simple docstring"""
     return self.head is None







  def __str__(	self						):

     """simple docstring"""
     if self.is_empty():
        return ""
     else:
        UpperCAmelCase_      :      str      =					self.head
        UpperCAmelCase_      :      str      =					""
        UpperCAmelCase_      :      list[str]      =					[]
        while iterate:
           item_list.append(str(iterate.item						)						)
           UpperCAmelCase_      :      Tuple      =					iterate.next

        UpperCAmelCase_      :      Optional[Any]      =					" --> ".join(lowercase_						)

        return item_str







  def __len__(	self						):

     """simple docstring"""
     return self.size


