



"""simple docstring"""
from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_lowerCAmelCase    :Dict     =					299_792_458

# Symbols
_lowerCAmelCase    :Any     =					symbols('ct x y z')





def  lowerCamelCase_						(UpperCamelCase__		:		int							):
    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__		:		Optional[Any]							):
    return 1 / sqrt(1 - beta(lowerCamelCase_							) ** 2							)





def  lowerCamelCase_						(UpperCamelCase__		:		Optional[Any]							):
    return np.array(
        [
            [gamma(lowerCamelCase_							), -gamma(lowerCamelCase_							) * beta(lowerCamelCase_							), 0, 0],
            [-gamma(lowerCamelCase_							) * beta(lowerCamelCase_							), gamma(lowerCamelCase_							), 0, 0],
            [0, 0, 1, 0],
            [0, 0, 0, 1],
        ]							)





def  lowerCamelCase_						(UpperCamelCase__		:		List[Any]     ,       UpperCamelCase__		:		Optional[int] = None							):
    # Ensure event is not empty
    if event is None:
        _UpperCAmelCase							:  int											=    np.array([ct, x, y, z]							)  # Symbolic four vector
    else:
        event[0] *= c  # x0 is ct (speed of light * time)

    return transformation_matrix(lowerCamelCase_							) @ event


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  # Example of symbolic vector:
  _lowerCAmelCase    :List[Any]     =					transform(29_979_245)
  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
  _lowerCAmelCase    :Tuple     =					{ct: c, x: 1, y: 1, z: 1}
  _lowerCAmelCase    :Optional[int]     =					[four_vector[i].subs(sub_dict) for i in range(4)]

  print(f"\n{numerical_vector}")










import warnings


warnings.warn(
    'memory_utils has been reorganized to utils.memory. Import `find_executable_batchsize` from the main `__init__`: '
    '`from accelerate import find_executable_batch_size` to avoid this warning.',
    FutureWarning,
)




