




lowerCamelCase__					:  int      							=				tuple[float, float, float]
lowerCamelCase__					:  Optional[Any]      							=				tuple[float, float, float]

def    UpperCAmelCase_				( __UpperCAmelCase		:      Pointad     ,     __UpperCAmelCase		:      Pointad				)   ->					Vectorad:
      SCREAMING_SNAKE_CASE_      		=     end_pointa[0] - end_pointa[0]
      SCREAMING_SNAKE_CASE_      		=     end_pointa[1] - end_pointa[1]
      SCREAMING_SNAKE_CASE_      		=     end_pointa[2] - end_pointa[2]
      return (x, y, z)

def    UpperCAmelCase_				( __UpperCAmelCase		:      Vectorad     ,     __UpperCAmelCase		:      Vectorad				)   ->					Vectorad:
      SCREAMING_SNAKE_CASE_      		=     ab[1] * ac[2] - ab[2] * ac[1]  # *i
      SCREAMING_SNAKE_CASE_      		=     (ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
      SCREAMING_SNAKE_CASE_      		=     ab[0] * ac[1] - ab[1] * ac[0]  # *k
      return (x, y, z)

def    UpperCAmelCase_				( __UpperCAmelCase		:      Vectorad     ,     __UpperCAmelCase		:      int				)   ->					bool:
      return tuple(round(__UpperCAmelCase     ,     __UpperCAmelCase				) for x in vector				) == (0, 0, 0)





def    UpperCAmelCase_				( __UpperCAmelCase		:      Pointad     ,     __UpperCAmelCase		:      Pointad     ,     __UpperCAmelCase		:      Pointad     ,     __UpperCAmelCase		:      int = 10				)   ->					bool:
      SCREAMING_SNAKE_CASE_      		=     create_vector(__UpperCAmelCase     ,     __UpperCAmelCase				)
      SCREAMING_SNAKE_CASE_      		=     create_vector(__UpperCAmelCase     ,     __UpperCAmelCase				)
      return is_zero_vector(get_ad_vectors_cross(__UpperCAmelCase     ,     __UpperCAmelCase				)     ,     __UpperCAmelCase				)






import numpy as np
def      A__       (    SCREAMING_SNAKE_CASE_   :      np.ndarray				,	SCREAMING_SNAKE_CASE_   :      float						)  ->  np.ndarray:






   """simple docstring"""







   return np.where(vector > 0				,	SCREAMING_SNAKE_CASE_				,	(alpha * (np.exp(SCREAMING_SNAKE_CASE_						) - 1))						)


if __name__ == "__main__":
   import doctest

   doctest.testmod()