from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_lowercase							:      Tuple      							=2_9_9_7_9_2_4_5_8

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



def A__  (			lowercase:     float					)				->		float:
       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:     float					)				->		float:
       return 1 / sqrt(1 - beta(lowercase					) ** 2					)



def A__  (			lowercase:     float					)				->		np.ndarray:
       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:     float,		lowercase:     np.ndarray | None = None					)				->		np.ndarray:
       # Ensure event is not empty
       if event is None:
              A						:     List[str]         =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:
    _lowercase							:      Dict      							=transform(2_9_9_7_9_2_4_5)
    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
    _lowercase							:      Dict      							={ct: c, x: 1, y: 1, z: 1}
    _lowercase							:      Dict      							=[four_vector[i].subs(sub_dict) for i in range(4)]

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







import logging
from dataclasses import dataclass, field
from typing import Optional

from seqaseq_trainer import arg_to_scheduler

from transformers import TrainingArguments


_lowercase							:      Any      							=logging.getLogger(__name__)



@dataclass
class  SCREAMING_SNAKE_CASE_ (					lowerCAmelCase_			):
  '''simple docstring'''


  lowercase		:     Optional[float]            =				field(
      default=0.0   ,						metadata={"help": "The label smoothing epsilon to apply (if not zero)."}			)
  lowercase		:     bool            =				field(default=lowerCAmelCase_   ,						metadata={"help": "Whether to SortishSamler or not."}			)
  lowercase		:     bool            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Whether to use generate to calculate generative metrics (ROUGE, BLEU)."}			)
  lowercase		:     bool            =				field(default=lowerCAmelCase_   ,						metadata={"help": "whether to use adafactor"}			)
  lowercase		:     Optional[float]            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Encoder layer dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[float]            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Decoder layer dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[float]            =				field(default=lowerCAmelCase_   ,						metadata={"help": "Dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[float]            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Attention dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[str]            =				field(
      default="linear"   ,						metadata={"help": f'Which lr scheduler to use. Selected in {sorted(arg_to_scheduler.keys()			)}'}   ,						)






