


'''simple docstring'''






# 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 		_A			(lowerCAmelCase__					:List[str]						)				->					Dict:




     '''simple docstring'''



     return 1 / (1 + np.exp(-z						))






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




     '''simple docstring'''



     return (-y * np.log(__lowerCamelCase						) - (1 - y) * np.log(1 - h						)).mean()






def 		_A			(lowerCAmelCase__					:Any			,  lowerCAmelCase__					:List[str]			,  lowerCAmelCase__					:str						)				->					Dict:




     '''simple docstring'''



     _a      =							np.dot(__lowerCamelCase			,  __lowerCamelCase						)
     return np.sum(y * scores - np.log(1 + np.exp(__lowerCamelCase						)						)						)






def 		_A			(lowerCAmelCase__					:List[str]			,  lowerCAmelCase__					:List[str]			,  lowerCAmelCase__					:str			,  lowerCAmelCase__					:Optional[Any]=7_00_00						)				->					List[str]:




     '''simple docstring'''



     _a      =							np.zeros(x.shape[1]						)

     for iterations in range(__lowerCamelCase						):
          _a      =							np.dot(__lowerCamelCase			,  __lowerCamelCase						)
          _a      =							sigmoid_function(__lowerCamelCase						)
          _a      =							np.dot(x.T			,  h - y						) / y.size
          _a      =							theta - alpha * gradient  # updating the weights
          _a      =							np.dot(__lowerCamelCase			,  __lowerCamelCase						)
          _a      =							sigmoid_function(__lowerCamelCase						)
          _a      =							cost_function(__lowerCamelCase			,  __lowerCamelCase						)
          if iterations % 1_00 == 0:
               print(f'loss: {j} \t'						)  # printing the loss after every 100 iterations
     return theta


# In[68]:

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

 a_   :      Optional[int]				    =      0.1
 a_   :      Tuple				    =      logistic_reg(alpha, x, y, max_iterations=7_0_0_0_0)
 print("theta: ", theta)  # printing the theta i.e our weights vector






 def 		_A			(lowerCAmelCase__					:int						)				->					str:




      '''simple docstring'''



      return sigmoid_function(
          np.dot(__lowerCamelCase			,  __lowerCamelCase						)						)  # predicting the value of probability from the logistic regression algorithm

 plt.figure(figsize=(1_0, 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_))   :      Optional[Any]				    =      (x[:, 0].min(), x[:, 0].max())
 ((a_)    ,							(a_))   :      Optional[int]				    =      (x[:, 1].min(), x[:, 1].max())
 ((a_)    ,							(a_))   :      Union[str, Any]				    =      np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
 a_   :      Dict				    =      np.c_[xxa.ravel(), xxa.ravel()]
 a_   :      Any				    =      predict_prob(grid).reshape(xxa.shape)
 plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors="black")

 plt.legend()






 plt.show()






'''simple docstring'''






from __future__ import annotations






def 		_A			(lowerCAmelCase__					:int						)				->					list[int]:




     '''simple docstring'''



     _a      =							2
     _a      =							[]
     while i * i <= n:
          if n % i:
               i += 1
          else:
               n //= i
               factors.append(lowerCAmelCase__						)
     if n > 1:
          factors.append(lowerCAmelCase__						)
     return factors


if __name__ == "__main__":
 import doctest

 doctest.testmod()

