



"""simple docstring"""





import numpy as np
def   a__      ( lowerCAmelCase__ ):
      return (2 / (1 + np.exp(-2 * vector ))) - 1


if __name__ == "__main__":
  import doctest

  doctest.testmod()








'''simple docstring'''
def       a_				(	UpperCamelCase_ ):

							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))





