





from math import sqrt

import numpy as np
from sympy import symbols

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

# Symbols
UpperCAmelCase_       ,     UpperCAmelCase_       ,     UpperCAmelCase_       ,     UpperCAmelCase_           =	symbols("ct x y z")
def      A__       (    SCREAMING_SNAKE_CASE_   :      float						)  ->  float:






   """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      A__       (    SCREAMING_SNAKE_CASE_   :      float						)  ->  float:






   """simple docstring"""







   return 1 / sqrt(1 - beta(SCREAMING_SNAKE_CASE_						) ** 2						)
def      A__       (    SCREAMING_SNAKE_CASE_   :      float						)  ->  np.ndarray:






   """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      A__       (    SCREAMING_SNAKE_CASE_   :      float				,	SCREAMING_SNAKE_CASE_   :      np.ndarray | None = None						)  ->  np.ndarray:






   """simple docstring"""







   if event is None:
      _UpperCAmelCase           =   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_           =	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
   UpperCAmelCase_           =	{ct: c, x: 1, y: 1, z: 1}
   UpperCAmelCase_           =	[four_vector[i].subs(sub_dict) for i in range(4)]

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






from typing import TYPE_CHECKING

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


UpperCAmelCase_           =	{
    "configuration_xlm": ["XLM_PRETRAINED_CONFIG_ARCHIVE_MAP", "XLMConfig", "XLMOnnxConfig"],
    "tokenization_xlm": ["XLMTokenizer"],
}

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase_           =	[
       "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:
   UpperCAmelCase_           =	[
       "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

   UpperCAmelCase_           =	_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)