
"""simple docstring"""





_a														=		8.314_4598



def       lowerCamelCase__		(			__snake_case,     __snake_case	)							->		float:


					"""simple docstring"""





					if temperature < 0:
										raise Exception('''Temperature cannot be less than 0 K'''	)
					if molar_mass <= 0:
										raise Exception('''Molar mass cannot be less than or equal to 0 kg/mol'''	)
					else:
										return (3 * UNIVERSAL_GAS_CONSTANT * temperature / molar_mass) ** 0.5


if __name__ == "__main__":
				import doctest

				# run doctest
				doctest.testmod()

				# example
				_a														=		300
				_a														=		28
				_a														=		rms_speed_of_molecule(temperature, molar_mass)
				print(F"""Vrms of Nitrogen gas at 300 K is {vrms} m/s""")








"""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__		(			__snake_case	)							->		Tuple:


					"""simple docstring"""





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



def       lowerCamelCase__		(			__snake_case,     __snake_case	)							->		List[str]:


					"""simple docstring"""





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



def       lowerCamelCase__		(			__snake_case,     __snake_case,     __snake_case	)							->		int:


					"""simple docstring"""





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



def       lowerCamelCase__		(			__snake_case,     __snake_case,     __snake_case,     __snake_case=7_00_00	)							->		Union[str, Any]:


					"""simple docstring"""





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

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

				_a														=		0.1
				_a														=		logistic_reg(alpha, x, y, max_iterations=7_0000)
				print("""theta: """, theta)  # printing the theta i.e our weights vector



				def       lowerCamelCase__		(			__snake_case	)							->		Tuple:


									"""simple docstring"""





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

				plt.legend()
				plt.show()






