



import numpy as np
import requests






def 						_lowerCAmelCase    (					):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     Any							=						requests.get(
     "https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/"
     "master/Week1/ADRvsRating.csv"  )
 __SCREAMING_SNAKE_CASE							:     Tuple							=						response.text.splitlines()
 __SCREAMING_SNAKE_CASE							:     List[str]							=						[]
 for item in lines:
  __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						item.split(","  )
  data.append(__lowerCamelCase  )
 data.pop(0  )  # This is for removing the labels from the list
 __SCREAMING_SNAKE_CASE							:     List[str]							=						np.matrix(__lowerCamelCase  )
 return dataset






def 						_lowerCAmelCase    (					__lowerCamelCase :  int		,						__lowerCamelCase :  Any		,						__lowerCamelCase :  Tuple		,						__lowerCamelCase :  Union[str, Any]		,						__lowerCamelCase :  Optional[int]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     List[Any]							=						len_data

 __SCREAMING_SNAKE_CASE							:     Dict							=						np.dot(__lowerCamelCase		,						data_x.transpose()  )
 prod -= data_y.transpose()
 __SCREAMING_SNAKE_CASE							:     List[str]							=						np.dot(__lowerCamelCase		,						__lowerCamelCase  )
 __SCREAMING_SNAKE_CASE							:     Union[str, Any]							=						theta - (alpha / n) * sum_grad
 return theta






def 						_lowerCAmelCase    (					__lowerCamelCase :  Tuple		,						__lowerCamelCase :  Optional[int]		,						__lowerCamelCase :  str		,						__lowerCamelCase :  List[Any]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     Tuple							=						np.dot(__lowerCamelCase		,						data_x.transpose()  )
 prod -= data_y.transpose()
 __SCREAMING_SNAKE_CASE							:     Dict							=						np.sum(np.square(__lowerCamelCase  )  )
 __SCREAMING_SNAKE_CASE							:     Dict							=						sum_elem / (2 * len_data)
 return error






def 						_lowerCAmelCase    (					__lowerCamelCase :  Any		,						__lowerCamelCase :  List[str]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     List[Any]							=						100000
 __SCREAMING_SNAKE_CASE							:     int							=						0.0001550

 __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						data_x.shape[1]
 __SCREAMING_SNAKE_CASE							:     Any							=						data_x.shape[0] - 1

 __SCREAMING_SNAKE_CASE							:     Any							=						np.zeros((1, no_features)  )

 for i in range(0		,						__lowerCamelCase  ):
  __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						run_steep_gradient_descent(__lowerCamelCase		,						__lowerCamelCase		,						__lowerCamelCase		,						__lowerCamelCase		,						__lowerCamelCase  )
  __SCREAMING_SNAKE_CASE							:     List[Any]							=						sum_of_square_error(__lowerCamelCase		,						__lowerCamelCase		,						__lowerCamelCase		,						__lowerCamelCase  )
  print(F"""At Iteration {i + 1} - Error is {error:.5f}"""  )

 return theta






def 						_lowerCAmelCase    (					__lowerCamelCase :  Dict		,						__lowerCamelCase :  Optional[Any]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     int							=						sum(abs(y - predicted_y[i]  ) for i, y in enumerate(__lowerCamelCase  )  )
 return total / len(__lowerCamelCase  )






def 						_lowerCAmelCase    (					):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     Optional[int]							=						collect_dataset()

 __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						data.shape[0]
 __SCREAMING_SNAKE_CASE							:     Union[str, Any]							=						np.c_[np.ones(__lowerCamelCase  ), data[:, :-1]].astype(__lowerCamelCase  )
 __SCREAMING_SNAKE_CASE							:     Any							=						data[:, -1].astype(__lowerCamelCase  )

 __SCREAMING_SNAKE_CASE							:     List[Any]							=						run_linear_regression(__lowerCamelCase		,						__lowerCamelCase  )
 __SCREAMING_SNAKE_CASE							:     Union[str, Any]							=						theta.shape[1]
 print("Resultant Feature vector : "  )
 for i in range(0		,						__lowerCamelCase  ):
  print(F"""{theta[0, i]:.5f}"""  )


if __name__ == "__main__":
      main()











'''simple docstring'''







import matplotlib.pyplot as plt
import numpy as np







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

		return weights







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:int										=      weight_matrix(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     )
		SCREAMING_SNAKE_CASE_						:str										=      np.linalg.inv(x_train.T @ weight_mat @ x_train     ) @ (
		    x_train.T @ weight_mat @ y_train.T
		)

		return weight







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:int										=      np.zeros(len(SCREAMING_SNAKE_CASE     )     )  # Initialize array of predictions
		for i, item in enumerate(SCREAMING_SNAKE_CASE     ):
				SCREAMING_SNAKE_CASE_						:Dict										=      item @ local_weight(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     )

		return y_pred







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		import seaborn as sns

		SCREAMING_SNAKE_CASE_						:Union[str, Any]										=      sns.load_dataset(SCREAMING_SNAKE_CASE     )
		SCREAMING_SNAKE_CASE_						:Tuple										=      np.array(data[x_name]     )
		SCREAMING_SNAKE_CASE_						:Optional[int]										=      np.array(data[y_name]     )

		SCREAMING_SNAKE_CASE_						:str										=      np.ones(len(SCREAMING_SNAKE_CASE     )     )

		# pairing elements of one and x_data
		SCREAMING_SNAKE_CASE_						:Optional[int]										=      np.column_stack((one, x_data)     )

		return x_train, x_data, y_data







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		):
		SCREAMING_SNAKE_CASE_						:Tuple										=      np.sort(SCREAMING_SNAKE_CASE ,		axis=0     )
		plt.scatter(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		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(SCREAMING_SNAKE_CASE     )
		plt.ylabel(SCREAMING_SNAKE_CASE     )
		plt.show()


if __name__ == "__main__":
							import doctest

							doctest.testmod()

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