


def 						_A						(						_lowercase			,       _lowercase				)			->				int:


     """simple docstring"""


     if not root or root not in binary_tree_mirror_dictionary:
          return
     __UpperCamelCase,  __UpperCamelCase				=	binary_tree_mirror_dictionary[root][:2]
     __UpperCamelCase				=	[right_child, left_child]
     binary_tree_mirror_dict(_lowercase			,       _lowercase				)
     binary_tree_mirror_dict(_lowercase			,       _lowercase				)






def 						_A						(						_lowercase			,       _lowercase = 1				)			->				dict:


     """simple docstring"""


     if not binary_tree:
          raise ValueError('binary tree cannot be empty'				)
     if root not in binary_tree:
          __UpperCamelCase				=	f'''root {root} is not present in the binary_tree'''
          raise ValueError(_lowercase				)
     __UpperCamelCase				=	dict(_lowercase				)
     binary_tree_mirror_dict(_lowercase			,       _lowercase				)
     return binary_tree_mirror_dictionary


if __name__ == "__main__":
    __snake_case     =		{1: [2, 3], 2: [4, 5], 3: [6, 7], 7: [8, 9]}
    print(f"""Binary tree: {binary_tree}""")
    __snake_case     =		binary_tree_mirror(binary_tree, 5)
    print(f"""Binary tree mirror: {binary_tree_mirror_dictionary}""")






import matplotlib.pyplot as plt
import numpy as np






def 						_A						(						_lowercase			,       _lowercase			,       _lowercase				)			->				np.ndarray:


     """simple docstring"""


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

     return weights






def 						_A						(						_lowercase			,       _lowercase			,       _lowercase			,       _lowercase				)			->				np.ndarray:


     """simple docstring"""


     __UpperCamelCase				=	weight_matrix(_lowercase			,       _lowercase			,       _lowercase				)
     __UpperCamelCase				=	np.linalg.inv(x_train.T @ weight_mat @ x_train				) @ (
         x_train.T @ weight_mat @ y_train.T
     )

     return weight






def 						_A						(						_lowercase			,       _lowercase			,       _lowercase				)			->				np.ndarray:


     """simple docstring"""


     __UpperCamelCase				=	np.zeros(len(_lowercase				)				)  # Initialize array of predictions
     for i, item in enumerate(_lowercase				):
          __UpperCamelCase				=	item @ local_weight(_lowercase			,       _lowercase			,       _lowercase			,       _lowercase				)

     return y_pred






def 						_A						(						_lowercase			,       _lowercase			,       _lowercase				)			->				tuple[np.ndarray, np.ndarray, np.ndarray]:


     """simple docstring"""


     import seaborn as sns

     __UpperCamelCase				=	sns.load_dataset(_lowercase				)
     __UpperCamelCase				=	np.array(data[x_name]				)
     __UpperCamelCase				=	np.array(data[y_name]				)

     __UpperCamelCase				=	np.ones(len(_lowercase				)				)

     # pairing elements of one and x_data
     __UpperCamelCase				=	np.column_stack((one, x_data)				)

     return x_train, x_data, y_data






def 						_A						(						_lowercase			,       _lowercase			,       _lowercase			,       _lowercase			,       _lowercase			,       _lowercase			,       )			->				None:


     """simple docstring"""


     __UpperCamelCase				=	np.sort(_lowercase			,       axis=0				)
     plt.scatter(_lowercase			,       _lowercase			,       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(_lowercase				)
     plt.ylabel(_lowercase				)
     plt.show()


if __name__ == "__main__":
    import doctest

    doctest.testmod()

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


