"""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      lowerCamelCase_(__SCREAMING_SNAKE_CASE  )->    Optional[int]:
							return 1 / (1 + np.exp(-z  ))



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



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )->    Any:
							_SCREAMING_SNAKE_CASE		:						List[Any]			  =    np.dot(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )
							return np.sum(y * scores - np.log(1 + np.exp(__SCREAMING_SNAKE_CASE  )  )  )



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE=70_000  )->    Optional[int]:
							_SCREAMING_SNAKE_CASE		:						Tuple			  =    np.zeros(x.shape[1]  )

							for iterations in range(__SCREAMING_SNAKE_CASE  ):
														_SCREAMING_SNAKE_CASE		:						Tuple			  =    np.dot(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )
														_SCREAMING_SNAKE_CASE		:						List[Any]			  =    sigmoid_function(__SCREAMING_SNAKE_CASE  )
														_SCREAMING_SNAKE_CASE		:						Union[str, Any]			  =    np.dot(x.T     ,	h - y  ) / y.size
														_SCREAMING_SNAKE_CASE		:						Any			  =    theta - alpha * gradient  # updating the weights
														_SCREAMING_SNAKE_CASE		:						Optional[Any]			  =    np.dot(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )
														_SCREAMING_SNAKE_CASE		:						Optional[int]			  =    sigmoid_function(__SCREAMING_SNAKE_CASE  )
														_SCREAMING_SNAKE_CASE		:						List[Any]			  =    cost_function(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_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__":
			lowerCAmelCase_     =	datasets.load_iris()
			lowerCAmelCase_     =	iris.data[:, :2]
			lowerCAmelCase_     =	(iris.target != 0) * 1

			lowerCAmelCase_     =	0.1
			lowerCAmelCase_     =	logistic_reg(alpha, x, y, max_iterations=70000)
			print('''theta: ''', theta)  # printing the theta i.e our weights vector



			def      lowerCamelCase_(__SCREAMING_SNAKE_CASE  )->    List[Any]:
										return sigmoid_function(
										    np.dot(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_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''')
			((lowerCAmelCase_) ,					(lowerCAmelCase_))     =	(x[:, 0].min(), x[:, 0].max())
			((lowerCAmelCase_) ,					(lowerCAmelCase_))     =	(x[:, 1].min(), x[:, 1].max())
			((lowerCAmelCase_) ,					(lowerCAmelCase_))     =	np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
			lowerCAmelCase_     =	np.c_[xxa.ravel(), xxa.ravel()]
			lowerCAmelCase_     =	predict_prob(grid).reshape(xxa.shape)
			plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors='''black''')

			plt.legend()


			plt.show()



"""simple docstring"""





from typing import Any

import numpy as np



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE  )->    bool:
							return np.array_equal(__SCREAMING_SNAKE_CASE     ,	matrix.conjugate().T  )



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )->    Any:
							_SCREAMING_SNAKE_CASE		:						Optional[int]			  =    v.conjugate().T
							_SCREAMING_SNAKE_CASE		:						Optional[int]			  =    v_star.dot(__SCREAMING_SNAKE_CASE  )
							assert isinstance(__SCREAMING_SNAKE_CASE     ,	np.ndarray  )
							return (v_star_dot.dot(__SCREAMING_SNAKE_CASE  )) / (v_star.dot(__SCREAMING_SNAKE_CASE  ))



def      lowerCamelCase_()->    None:
							_SCREAMING_SNAKE_CASE		:						Optional[Any]			  =    np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]  )
							_SCREAMING_SNAKE_CASE		:						int			  =    np.array([[1], [2], [3]]  )
							assert is_hermitian(__SCREAMING_SNAKE_CASE  ), F"""{a} is not hermitian."""
							print(rayleigh_quotient(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )  )

							_SCREAMING_SNAKE_CASE		:						int			  =    np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]  )
							assert is_hermitian(__SCREAMING_SNAKE_CASE  ), F"""{a} is not hermitian."""
							assert rayleigh_quotient(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  ) == float(3  )


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			tests()


