



import math

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :int							)     ->    list:
   if n <= 0:
      raise ValueError('''Only positive integers have prime factors'''							)
   _A						     =					[]
   while n % 2 == 0:
      pf.append(2							)
      _A						     =					int(n / 2							)
   for i in range(3  ,      int(math.sqrt(_snake_case							)							) + 1  ,      2							):
      while n % i == 0:
         pf.append(_snake_case							)
         _A						     =					int(n / i							)
   if n > 2:
      pf.append(_snake_case							)
   return pf

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :int							)     ->    int:
   if n <= 0:
      raise ValueError('''Only positive numbers are accepted'''							)
   _A						     =					1
   _A						     =					1
   while n % 2 == 0:
      temp += 1
      _A						     =					int(n / 2							)
   div *= temp
   for i in range(3  ,      int(math.sqrt(_snake_case							)							) + 1  ,      2							):
      _A						     =					1
      while n % i == 0:
         temp += 1
         _A						     =					int(n / i							)
      div *= temp
   if n > 1:
      div *= 2
   return div

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :int							)     ->    int:
   if n <= 0:
      raise ValueError('''Only positive numbers are accepted'''							)
   _A						     =					1
   _A						     =					1
   while n % 2 == 0:
      temp += 1
      _A						     =					int(n / 2							)
   if temp > 1:
      s *= (2**temp - 1) / (2 - 1)
   for i in range(3  ,      int(math.sqrt(_snake_case							)							) + 1  ,      2							):
      _A						     =					1
      while n % i == 0:
         temp += 1
         _A						     =					int(n / i							)
      if temp > 1:
         s *= (i**temp - 1) / (i - 1)
   return int(_snake_case							)

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :int							)     ->    int:
   _A						     =					n
   for x in set(prime_factors(_snake_case							)							):
      s *= (x - 1) / x
   return int(_snake_case							)


if __name__ == "__main__":
   import doctest

   doctest.testmod()








import numpy as np
import requests

def   SCREAMING_SNAKE_CASE_       (  )     ->    Any:
   _A						     =					requests.get(
       '''https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/'''
       '''master/Week1/ADRvsRating.csv'''							)
   _A						     =					response.text.splitlines()
   _A						     =					[]
   for item in lines:
      _A						     =					item.split(''','''							)
      data.append(_snake_case							)
   data.pop(0							)  # This is for removing the labels from the list
   _A						     =					np.matrix(_snake_case							)
   return dataset

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :int  ,      _snake_case  :Dict  ,      _snake_case  :Tuple  ,      _snake_case  :Tuple  ,      _snake_case  :str							)     ->    int:
   _A						     =					len_data

   _A						     =					np.dot(_snake_case  ,      data_x.transpose()							)
   prod -= data_y.transpose()
   _A						     =					np.dot(_snake_case  ,      _snake_case							)
   _A						     =					theta - (alpha / n) * sum_grad
   return theta

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :Union[str, Any]  ,      _snake_case  :Any  ,      _snake_case  :Optional[Any]  ,      _snake_case  :List[Any]							)     ->    Tuple:
   _A						     =					np.dot(_snake_case  ,      data_x.transpose()							)
   prod -= data_y.transpose()
   _A						     =					np.sum(np.square(_snake_case							)							)
   _A						     =					sum_elem / (2 * len_data)
   return error

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :Union[str, Any]  ,      _snake_case  :Union[str, Any]							)     ->    List[str]:
   _A						     =					100_000
   _A						     =					0.000_1550

   _A						     =					data_x.shape[1]
   _A						     =					data_x.shape[0] - 1

   _A						     =					np.zeros((1, no_features)							)

   for i in range(0  ,      _snake_case							):
      _A						     =					run_steep_gradient_descent(_snake_case  ,      _snake_case  ,      _snake_case  ,      _snake_case  ,      _snake_case							)
      _A						     =					sum_of_square_error(_snake_case  ,      _snake_case  ,      _snake_case  ,      _snake_case							)
      print(F'''At Iteration {i + 1} - Error is {error:.5f}'''							)

   return theta

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :List[Any]  ,      _snake_case  :Optional[int]							)     ->    Tuple:
   _A						     =					sum(abs(y - predicted_y[i]							) for i, y in enumerate(_snake_case							)							)
   return total / len(_snake_case							)

def   SCREAMING_SNAKE_CASE_       (  )     ->    Tuple:
   _A						     =					collect_dataset()

   _A						     =					data.shape[0]
   _A						     =					np.c_[np.ones(_snake_case							), data[:, :-1]].astype(_snake_case							)
   _A						     =					data[:, -1].astype(_snake_case							)

   _A						     =					run_linear_regression(_snake_case  ,      _snake_case							)
   _A						     =					theta.shape[1]
   print('''Resultant Feature vector : '''							)
   for i in range(0  ,      _snake_case							):
      print(F'''{theta[0, i]:.5f}'''							)


if __name__ == "__main__":
   main()



