






'''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  SCREAMING_SNAKE_CASE_       (UpperCamelCase      )      ->       List[str]:
							return 1 / (1 + np.exp(-z      ))





def  SCREAMING_SNAKE_CASE_       (UpperCamelCase				,			UpperCamelCase      )      ->       Tuple:
							return (-y * np.log(UpperCamelCase      ) - (1 - y) * np.log(1 - h      )).mean()





def  SCREAMING_SNAKE_CASE_       (UpperCamelCase				,			UpperCamelCase				,			UpperCamelCase      )      ->       Any:
							lowerCamelCase__					:	Any         =       np.dot(UpperCamelCase				,			UpperCamelCase      )
							return np.sum(y * scores - np.log(1 + np.exp(UpperCamelCase      )      )      )





def  SCREAMING_SNAKE_CASE_       (UpperCamelCase				,			UpperCamelCase				,			UpperCamelCase				,			UpperCamelCase=70000      )      ->       str:
							lowerCamelCase__					:	str         =       np.zeros(x.shape[1]      )

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


# In[68]:

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

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





			def  SCREAMING_SNAKE_CASE_       (UpperCamelCase      )      ->       Tuple:
										return sigmoid_function(
										    np.dot(UpperCamelCase				,			UpperCamelCase      )      )  # 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))	:			Tuple         =(x[:, 0].min(), x[:, 0].max())
			((_A)     ,      (_A))	:			int         =(x[:, 1].min(), x[:, 1].max())
			((_A)     ,      (_A))	:			List[Any]         =np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
			_A	:			int         =np.c_[xxa.ravel(), xxa.ravel()]
			_A	:			Optional[int]         =predict_prob(grid).reshape(xxa.shape)
			plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors='''black''')

			plt.legend()



			plt.show()








def 						__SCREAMING_SNAKE_CASE  (				UpperCamelCase__ )  ->				list[int]:







			'''simple docstring'''

			if length <= 0 or not isinstance(UpperCamelCase__			,			UpperCamelCase__ ):
						raise ValueError('''Length must be a positive integer.''' )
			return [n * (2 * n - 1) for n in range(UpperCamelCase__ )]


if __name__ == "__main__":
				print(hexagonal_numbers(length=5))
				print(hexagonal_numbers(length=10))



