


from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
snake_case__			 =						2_9979_2458

# Symbols
snake_case__			 =						symbols('''ct x y z''')


def 				lowerCamelCase__	(      a	:   float				)    ->	Optional[int]:





			"""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 				lowerCamelCase__	(      a	:   float				)    ->	Any:





			"""simple docstring"""
			return 1 / sqrt(1 - beta(UpperCAmelCase__				) ** 2				)


def 				lowerCamelCase__	(      a	:   float				)    ->	List[str]:





			"""simple docstring"""
			return np.array(
			    [
			        [gamma(UpperCAmelCase__				), -gamma(UpperCAmelCase__				) * beta(UpperCAmelCase__				), 0, 0],
			        [-gamma(UpperCAmelCase__				) * beta(UpperCAmelCase__				), gamma(UpperCAmelCase__				), 0, 0],
			        [0, 0, 1, 0],
			        [0, 0, 0, 1],
			    ]				)


def 				lowerCamelCase__	(      a	:   float	,  a	:   np.ndarray | None = None				)    ->	List[str]:





			"""simple docstring"""

			if event is None:
						a__ :Any						  =    np.array([ct, x, y, z]				)  # Symbolic four vector
			else:
						event[0] *= c  # x0 is ct (speed of light * time)

			return transformation_matrix(UpperCAmelCase__				) @ event


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		# Example of symbolic vector:
		snake_case__			 =						transform(2997_9245)
		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}''')






import importlib
import os
from dataclasses import dataclass
from enum import Enum
from typing import Any, Dict, Optional, Union

import torch

from ..utils import BaseOutput


snake_case__			 =						'''scheduler_config.json'''


class 					lowerCAmelCase_ (       _a):
						lowerCamelCase_         =     1
						lowerCamelCase_         =     2
						lowerCamelCase_         =     3
						lowerCamelCase_         =     4
						lowerCamelCase_         =     5
						lowerCamelCase_         =     6
						lowerCamelCase_         =     7
						lowerCamelCase_         =     8
						lowerCamelCase_         =     9
						lowerCamelCase_         =     10
						lowerCamelCase_         =     11
						lowerCamelCase_         =     12
						lowerCamelCase_         =     13
						lowerCamelCase_         =     14






@dataclass
class 					lowerCAmelCase_ (       _a):
						lowerCamelCase_         =     42






class 					lowerCAmelCase_ :
						lowerCamelCase_         =     SCHEDULER_CONFIG_NAME
						lowerCamelCase_         =     []
						lowerCamelCase_         =     True




						@classmethod
						def  _snake_case					(	cls						:   Union[str, Any]   ,     __A						:   Dict[str, Any] = None   ,     __A						:   Optional[str] = None   ,     __A						:   Optional[int]=False   ,     **__A						:   Union[str, Any]   ,     )      ->List[Any]:






									"""simple docstring"""






									a__  ,  a__  ,  a__ :List[Any]						  =    cls.load_config(
									    pretrained_model_name_or_path=__A   ,     subfolder=__A   ,     return_unused_kwargs=__A   ,     return_commit_hash=__A   ,     **__A   ,     )
									return cls.from_config(__A   ,     return_unused_kwargs=__A   ,     **__A						)




						def  _snake_case					(	self						:   str   ,     __A						:   Union[str, os.PathLike]   ,     __A						:   bool = False   ,     **__A						:   Optional[Any]						)      ->str:






									"""simple docstring"""






									self.save_config(save_directory=__A   ,     push_to_hub=__A   ,     **__A						)




						@property
						def  _snake_case					(	self						:   List[Any]						)      ->Dict:






									"""simple docstring"""






									return self._get_compatibles()






						@classmethod
						def  _snake_case					(	cls						:   Dict						)      ->int:






									"""simple docstring"""






									a__ :Optional[int]						  =    list(set([cls.__name__] + cls._compatibles						)						)
									a__ :Union[str, Any]						  =    importlib.import_module(__name__.split("."						)[0]						)
									a__ :Optional[int]						  =    [
									    getattr(__A   ,     __A						) for c in compatible_classes_str if hasattr(__A   ,     __A						)
									]
									return compatible_classes


