
"""simple docstring"""






from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
__SCREAMING_SNAKE_CASE							=     299_792_458

# Symbols
__SCREAMING_SNAKE_CASE				, __SCREAMING_SNAKE_CASE				, __SCREAMING_SNAKE_CASE				, __SCREAMING_SNAKE_CASE							=     symbols('ct x y z')




def       A_  (				__lowercase	):
 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       A_  (				__lowercase	):
 return 1 / sqrt(1 - beta(__lowercase	) ** 2	)




def       A_  (				__lowercase	):
 return np.array(
     [
         [gamma(__lowercase	), -gamma(__lowercase	) * beta(__lowercase	), 0, 0],
         [-gamma(__lowercase	) * beta(__lowercase	), gamma(__lowercase	), 0, 0],
         [0, 0, 1, 0],
         [0, 0, 0, 1],
     ]	)




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

 return transformation_matrix(__lowercase	) @ event


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # Example of symbolic vector:
 __SCREAMING_SNAKE_CASE							=     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
 __SCREAMING_SNAKE_CASE							=     {ct: c, x: 1, y: 1, z: 1}
 __SCREAMING_SNAKE_CASE							=     [four_vector[i].subs(sub_dict) for i in range(4)]

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


"""simple docstring"""






from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_torch_available,
)


__SCREAMING_SNAKE_CASE							=     {
    'configuration_mega': ['MEGA_PRETRAINED_CONFIG_ARCHIVE_MAP', 'MegaConfig', 'MegaOnnxConfig'],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __SCREAMING_SNAKE_CASE							=     [
     'MEGA_PRETRAINED_MODEL_ARCHIVE_LIST',
     'MegaForCausalLM',
     'MegaForMaskedLM',
     'MegaForMultipleChoice',
     'MegaForQuestionAnswering',
     'MegaForSequenceClassification',
     'MegaForTokenClassification',
     'MegaModel',
     'MegaPreTrainedModel',
 ]

if TYPE_CHECKING:
 from .configuration_mega import MEGA_PRETRAINED_CONFIG_ARCHIVE_MAP, MegaConfig, MegaOnnxConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_mega import (
      MEGA_PRETRAINED_MODEL_ARCHIVE_LIST,
      MegaForCausalLM,
      MegaForMaskedLM,
      MegaForMultipleChoice,
      MegaForQuestionAnswering,
      MegaForSequenceClassification,
      MegaForTokenClassification,
      MegaModel,
      MegaPreTrainedModel,
  )

else:
 import sys

 __SCREAMING_SNAKE_CASE							=     _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
