




# 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(       UpperCamelCase__							:			List[Any]				)    -> Union[str, Any]:
							'''simple docstring'''


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







def 		_A(       UpperCamelCase__							:			Optional[Any]				,       UpperCamelCase__							:			Optional[Any]				)    -> int:
							'''simple docstring'''


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







def 		_A(       UpperCamelCase__							:			Dict				,       UpperCamelCase__							:			Any				,       UpperCamelCase__							:			Tuple				)    -> List[Any]:
							'''simple docstring'''


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







def 		_A(       UpperCamelCase__							:			Tuple				,       UpperCamelCase__							:			Optional[int]				,       UpperCamelCase__							:			List[str]				,       UpperCamelCase__							:			Optional[int]=7_0000				)    -> Tuple:
							'''simple docstring'''


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

							for iterations in range(UpperCamelCase__				):
														__lowercase      =    np.dot(UpperCamelCase__				,       UpperCamelCase__				)
														__lowercase      =    sigmoid_function(UpperCamelCase__				)
														__lowercase      =    np.dot(x.T				,       h - y				) / y.size
														__lowercase      =    theta - alpha * gradient  # updating the weights
														__lowercase      =    np.dot(UpperCamelCase__				,       UpperCamelCase__				)
														__lowercase      =    sigmoid_function(UpperCamelCase__				)
														__lowercase      =    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 		_A(       UpperCamelCase__							:			Optional[int]				)    -> List[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()












from __future__ import annotations







def 		_A(       UpperCamelCase__							:			list[int]				,       UpperCamelCase__							:			list[int]				,       UpperCamelCase__							:			int				)    -> tuple[float, list[float]]:
							'''simple docstring'''


							__lowercase      =    list(range(len(UpperCamelCase__				)				)				)
							__lowercase      =    [v / w for v, w in zip(UpperCamelCase__				,       UpperCamelCase__				)]
							index.sort(key=lambda UpperCamelCase__				: ratio[i]				,       reverse=UpperCamelCase__				)

							__lowercase      =    0
							__lowercase      =    [0] * len(UpperCamelCase__				)
							for i in index:
														if weight[i] <= capacity:
																					__lowercase      =    1
																					max_value += value[i]
																					capacity -= weight[i]
														else:
																					__lowercase      =    capacity / weight[i]
																					max_value += value[i] * capacity / weight[i]
																					break

							return max_value, fractions


if __name__ == "__main__":
			import doctest

			doctest.testmod()






