
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


__a  			=					{
    'configuration_xlm': ['XLM_PRETRAINED_CONFIG_ARCHIVE_MAP', 'XLMConfig', 'XLMOnnxConfig'],
    'tokenization_xlm': ['XLMTokenizer'],
}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__a  			=					[
						    'XLM_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'XLMForMultipleChoice',
						    'XLMForQuestionAnswering',
						    'XLMForQuestionAnsweringSimple',
						    'XLMForSequenceClassification',
						    'XLMForTokenClassification',
						    'XLMModel',
						    'XLMPreTrainedModel',
						    'XLMWithLMHeadModel',
						]

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__a  			=					[
						    'TF_XLM_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'TFXLMForMultipleChoice',
						    'TFXLMForQuestionAnsweringSimple',
						    'TFXLMForSequenceClassification',
						    'TFXLMForTokenClassification',
						    'TFXLMMainLayer',
						    'TFXLMModel',
						    'TFXLMPreTrainedModel',
						    'TFXLMWithLMHeadModel',
						]


if TYPE_CHECKING:
						from .configuration_xlm import XLM_PRETRAINED_CONFIG_ARCHIVE_MAP, XLMConfig, XLMOnnxConfig
						from .tokenization_xlm import XLMTokenizer

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_xlm import (
												    XLM_PRETRAINED_MODEL_ARCHIVE_LIST,
												    XLMForMultipleChoice,
												    XLMForQuestionAnswering,
												    XLMForQuestionAnsweringSimple,
												    XLMForSequenceClassification,
												    XLMForTokenClassification,
												    XLMModel,
												    XLMPreTrainedModel,
												    XLMWithLMHeadModel,
												)

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_xlm import (
												    TF_XLM_PRETRAINED_MODEL_ARCHIVE_LIST,
												    TFXLMForMultipleChoice,
												    TFXLMForQuestionAnsweringSimple,
												    TFXLMForSequenceClassification,
												    TFXLMForTokenClassification,
												    TFXLMMainLayer,
												    TFXLMModel,
												    TFXLMPreTrainedModel,
												    TFXLMWithLMHeadModel,
												)

else:
						import sys

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








from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_snake_case             =     2_99_79_24_58

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






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''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 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

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






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''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 		lowercase_(  SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_ = None	):


  '''simple docstring'''

  if event is None:
    lowerCamelCase :					Tuple    =				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:
   _snake_case             =     transform(29_97_92_45)
   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
   _snake_case             =     {ct: c, x: 1, y: 1, z: 1}
   _snake_case             =     [four_vector[i].subs(sub_dict) for i in range(4)]

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



