






import matplotlib.pyplot as plt
import numpy as np
def        a_	( _A ,				_A ,				_A					)     ->     np.ndarray:







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

				return weights
def        a_	( _A ,				_A ,				_A ,				_A					)     ->     np.ndarray:







				"""simple docstring"""
				snake_case__													=       weight_matrix(_A ,				_A ,				_A					)
				snake_case__													=       np.linalg.inv(x_train.T @ weight_mat @ x_train					) @ (
				    x_train.T @ weight_mat @ y_train.T
				)

				return weight
def        a_	( _A ,				_A ,				_A					)     ->     np.ndarray:







				"""simple docstring"""
				snake_case__													=       np.zeros(len(_A					)					)  # Initialize array of predictions
				for i, item in enumerate(_A					):
								snake_case__													=       item @ local_weight(_A ,				_A ,				_A ,				_A					)

				return y_pred
def        a_	( _A ,				_A ,				_A					)     ->     tuple[np.ndarray, np.ndarray, np.ndarray]:







				"""simple docstring"""
				import seaborn as sns

				snake_case__													=       sns.load_dataset(_A					)
				snake_case__													=       np.array(data[x_name]					)
				snake_case__													=       np.array(data[y_name]					)

				snake_case__													=       np.ones(len(_A					)					)

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

				return x_train, x_data, y_data
def        a_	( _A ,				_A ,				_A ,				_A ,				_A ,				_A ,				)     ->     None:







				"""simple docstring"""
				snake_case__													=       np.sort(_A ,				axis=0					)
				plt.scatter(_A ,				_A ,				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(_A					)
				plt.ylabel(_A					)
				plt.show()


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							# Demo with a dataset from the seaborn module
							__UpperCamelCase					,  __UpperCamelCase					,  __UpperCamelCase   :						str							=  load_data("""tips""", """total_bill""", """tip""")
							__UpperCamelCase   :						List[Any]							=  local_weight_regression(training_data_x, tip, 5)
							plot_preds(training_data_x, predictions, total_bill, tip, """total_bill""", """tip""")












def        a_	( _A ,				_A					)     ->     Union[str, Any]:







				"""simple docstring"""
				snake_case__													=       1
				while b > 0:
								if b & 1:
												res *= a

								a *= a
								b >>= 1

				return res
def        a_	( _A ,				_A ,				_A					)     ->     Dict:







				"""simple docstring"""
				snake_case__													=       1
				while b > 0:
								if b & 1:
												snake_case__													=       ((res % c) * (a % c)) % c

								a *= a
								b >>= 1

				return res




