


# Logistic Regression from scratch

# In[62]:

# In[63]:

# importing all the required libraries

import numpy as np
from matplotlib import pyplot as plt
from sklearn import datasets



def     __lowerCAmelCase						(							snake_case	:    List[str] )       ->							str:
   return 1 / (1 + np.exp(-z ))



def     __lowerCAmelCase						(							snake_case	:    int						,      snake_case	:    int )       ->							Tuple:
   return (-y * np.log(snake_case ) - (1 - y) * np.log(1 - h )).mean()



def     __lowerCAmelCase						(							snake_case	:    List[Any]						,      snake_case	:    Tuple						,      snake_case	:    int )       ->							Union[str, Any]:
   __lowerCamelCase:				Dict     =	np.dot(snake_case						,      snake_case )
   return np.sum(y * scores - np.log(1 + np.exp(snake_case ) ) )



def     __lowerCAmelCase						(							snake_case	:    Tuple						,      snake_case	:    Dict						,      snake_case	:    Any						,      snake_case	:    str=70000 )       ->							List[Any]:
   __lowerCamelCase:				Tuple     =	np.zeros(x.shape[1] )

   for iterations in range(snake_case ):
      __lowerCamelCase:				List[str]     =	np.dot(snake_case						,      snake_case )
      __lowerCamelCase:				Any     =	sigmoid_function(snake_case )
      __lowerCamelCase:				Optional[Any]     =	np.dot(x.T						,      h - y ) / y.size
      __lowerCamelCase:				Dict     =	theta - alpha * gradient  # updating the weights
      __lowerCamelCase:				int     =	np.dot(snake_case						,      snake_case )
      __lowerCamelCase:				Optional[int]     =	sigmoid_function(snake_case )
      __lowerCamelCase:				Union[str, Any]     =	cost_function(snake_case						,      snake_case )
      if iterations % 100 == 0:
         print(f'loss: {j} \t' )  # printing the loss after every 100 iterations
   return theta


# In[68]:

if __name__ == "__main__":
   _A		:				List[Any]									=       datasets.load_iris()
   _A		:				str									=       iris.data[:, :2]
   _A		:				List[str]									=       (iris.target != 0) * 1

   _A		:				List[str]									=       0.1
   _A		:				List[str]									=       logistic_reg(alpha, x, y, max_iterations=70_000)
   print('''theta: ''', theta)  # printing the theta i.e our weights vector



   def     __lowerCAmelCase						(							snake_case	:    str )       ->							Dict:
      return sigmoid_function(
          np.dot(snake_case						,      snake_case ) )  # predicting the value of probability from the logistic regression algorithm

   plt.figure(figsize=(10, 6))
   plt.scatter(x[y == 0][:, 0], x[y == 0][:, 1], color='''b''', label='''0''')
   plt.scatter(x[y == 1][:, 0], x[y == 1][:, 1], color='''r''', label='''1''')
   ((_A)						,(_A))		:				List[str]									=       (x[:, 0].min(), x[:, 0].max())
   ((_A)						,(_A))		:				Tuple									=       (x[:, 1].min(), x[:, 1].max())
   ((_A)						,(_A))		:				List[str]									=       np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
   _A		:				Any									=       np.c_[xxa.ravel(), xxa.ravel()]
   _A		:				List[str]									=       predict_prob(grid).reshape(xxa.shape)
   plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors='''black''')

   plt.legend()







   plt.show()






def     __lowerCAmelCase						(							snake_case	:    int = 1000000 )       ->							int:
   __lowerCamelCase:				Union[str, Any]     =	set(range(3						,      snake_case						,      2 ) )
   primes.add(2 )
   for p in range(3						,      snake_case						,      2 ):
      if p not in primes:
         continue
      primes.difference_update(set(range(p * p						,      snake_case						,      snake_case ) ) )

   __lowerCamelCase:				Any     =	[float(snake_case ) for n in range(limit + 1 )]

   for p in primes:
      for n in range(snake_case						,      limit + 1						,      snake_case ):
         phi[n] *= 1 - 1 / p

   return int(sum(phi[2:] ) )


if __name__ == "__main__":
   print(F"""{solution() = }""")


