

from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_UpperCAmelCase		:   Optional[int]										=       2_9979_2458

# Symbols
_UpperCAmelCase				,						_UpperCAmelCase				,						_UpperCAmelCase				,						_UpperCAmelCase		:   Optional[Any]										=       symbols("""ct x y z""")





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							if velocity > c:
														raise ValueError('Speed must not exceed light speed 299,792,458 [m/s]!'      )
							elif velocity < 1:
														# Usually the speed should be much higher than 1 (c order of magnitude)
														raise ValueError('Speed must be greater than or equal to 1!'      )

							return velocity / c





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							return 1 / sqrt(1 - beta(SCREAMING_SNAKE_CASE_      ) ** 2      )





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							return np.array(
							    [
							        [gamma(SCREAMING_SNAKE_CASE_      ), -gamma(SCREAMING_SNAKE_CASE_      ) * beta(SCREAMING_SNAKE_CASE_      ), 0, 0],
							        [-gamma(SCREAMING_SNAKE_CASE_      ) * beta(SCREAMING_SNAKE_CASE_      ), gamma(SCREAMING_SNAKE_CASE_      ), 0, 0],
							        [0, 0, 1, 0],
							        [0, 0, 0, 1],
							    ]      )





def 					__lowerCamelCase	( UpperCamelCase__   ,							UpperCamelCase__ = None      ):







							'''simple docstring'''






							if event is None:
														snake_case_							=    np.array([ct, x, y, z]      )  # Symbolic four vector
							else:
														event[0] *= c  # x0 is ct (speed of light * time)

							return transformation_matrix(SCREAMING_SNAKE_CASE_      ) @ event


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					# Example of symbolic vector:
					_UpperCAmelCase		:   List[Any]										=       transform(2997_9245)
					print("""Example of four vector: """)
					print(F'''ct\' = {four_vector[0]}''')
					print(F'''x\' = {four_vector[1]}''')
					print(F'''y\' = {four_vector[2]}''')
					print(F'''z\' = {four_vector[3]}''')

					# Substitute symbols with numerical values
					_UpperCAmelCase		:   List[Any]										=       {ct: c, x: 1, y: 1, z: 1}
					_UpperCAmelCase		:   Union[str, Any]										=       [four_vector[i].subs(sub_dict) for i in range(4)]

					print(F'''\n{numerical_vector}''')








from ..utils import DummyObject, requires_backends
class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      Any     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      Optional[int]     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      str     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      List[Any]     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      Optional[int]     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      Dict     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      Dict     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      Union[str, Any]     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      Optional[int]     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      Optional[Any]     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      Any     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      Optional[Any]     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



class 	UpperCAmelCase_					(					metaclass=UpperCamelCase    ):

   '''simple docstring'''




   __A :      int     		=		["flax"]






   def __init__(		self						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(self						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )






   @classmethod
   def _snake_case    (		cls						,				*__A						,				**__A ):






     """simple docstring"""





     requires_backends(cls						,				["flax"] )



