





"""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__       (       UpperCamelCase__     :    Dict  )     ->	Dict:



					'''simple docstring'''




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





def   lowerCamelCase__       (       UpperCamelCase__     :    Union[str, Any]    ,      UpperCamelCase__     :    Optional[Any]  )     ->	str:



					'''simple docstring'''




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





def   lowerCamelCase__       (       UpperCamelCase__     :    Optional[Any]    ,      UpperCamelCase__     :    List[Any]    ,      UpperCamelCase__     :    List[Any]  )     ->	int:



					'''simple docstring'''




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





def   lowerCamelCase__       (       UpperCamelCase__     :    List[Any]    ,      UpperCamelCase__     :    int    ,      UpperCamelCase__     :    int    ,      UpperCamelCase__     :    Any=70_000  )     ->	Tuple:



					'''simple docstring'''




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

					for iterations in range(UpperCamelCase__  ):
										_snake_case													=			np.dot(UpperCamelCase__    ,      UpperCamelCase__  )
										_snake_case													=			sigmoid_function(UpperCamelCase__  )
										_snake_case													=			np.dot(x.T    ,      h - y  ) / y.size
										_snake_case													=			theta - alpha * gradient  # updating the weights
										_snake_case													=			np.dot(UpperCamelCase__    ,      UpperCamelCase__  )
										_snake_case													=			sigmoid_function(UpperCamelCase__  )
										_snake_case													=			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__":
					UpperCAmelCase_ 							=       datasets.load_iris()
					UpperCAmelCase_ 							=       iris.data[:, :2]
					UpperCAmelCase_ 							=       (iris.target != 0) * 1

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





					def   lowerCamelCase__       (       UpperCamelCase__     :    Dict  )     ->	Any:



										'''simple docstring'''




										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""")
					((UpperCAmelCase_)							, (UpperCAmelCase_)) 							=       (x[:, 0].min(), x[:, 0].max())
					((UpperCAmelCase_)							, (UpperCAmelCase_)) 							=       (x[:, 1].min(), x[:, 1].max())
					((UpperCAmelCase_)							, (UpperCAmelCase_)) 							=       np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
					UpperCAmelCase_ 							=       np.c_[xxa.ravel(), xxa.ravel()]
					UpperCAmelCase_ 							=       predict_prob(grid).reshape(xxa.shape)
					plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors="""black""")

					plt.legend()




					plt.show()










def   lowerCamelCase__       (       UpperCamelCase__     :    list[list[int]]    ,      UpperCamelCase__     :    int    ,      UpperCamelCase__     :    int    ,      UpperCamelCase__     :    list[int]  )     ->	bool:



					'''simple docstring'''




					if graph[path[curr_ind - 1]][next_ver] == 0:
										return False

					# 2. Validate that next vertex is not already in path
					return not any(vertex == next_ver for vertex in path  )





def   lowerCamelCase__       (       UpperCamelCase__     :    list[list[int]]    ,      UpperCamelCase__     :    list[int]    ,      UpperCamelCase__     :    int  )     ->	bool:



					'''simple docstring'''




					if curr_ind == len(UpperCamelCase__  ):
										# return whether path exists between current and starting vertices
										return graph[path[curr_ind - 1]][path[0]] == 1

					# Recursive Step
					for next_ver in range(0    ,      len(UpperCamelCase__  )  ):
										if valid_connection(UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__  ):
															# Insert current vertex  into path as next transition
															_snake_case													=			next_ver
															# Validate created path
															if util_hamilton_cycle(UpperCamelCase__    ,      UpperCamelCase__    ,      curr_ind + 1  ):
																				return True
															# Backtrack
															_snake_case													=			-1
					return False





def   lowerCamelCase__       (       UpperCamelCase__     :    list[list[int]]    ,      UpperCamelCase__     :    int = 0  )     ->	list[int]:



					'''simple docstring'''




					_snake_case													=			[-1] * (len(UpperCamelCase__  ) + 1)
					# initialize start and end of path with starting index
					_snake_case													=			_snake_case													=			start_index
					# evaluate and if we find answer return path either return empty array
					return path if util_hamilton_cycle(UpperCamelCase__    ,      UpperCamelCase__    ,      1  ) else []



