




from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
__UpperCamelCase   :			List[str]          = 299_792_458

# Symbols
__UpperCamelCase   ,    __UpperCamelCase   ,    __UpperCamelCase   ,    __UpperCamelCase   :			List[Any]          = symbols("ct x y z")





def 						__A						(      __lowerCamelCase       ) ->			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						(      __lowerCamelCase       ) ->			float:
	return 1 / sqrt(1 - beta(__lowerCamelCase       ) ** 2       )





def 						__A						(      __lowerCamelCase       ) ->			np.ndarray:
	return np.array(
	    [
	        [gamma(__lowerCamelCase       ), -gamma(__lowerCamelCase       ) * beta(__lowerCamelCase       ), 0, 0],
	        [-gamma(__lowerCamelCase       ) * beta(__lowerCamelCase       ), gamma(__lowerCamelCase       ), 0, 0],
	        [0, 0, 1, 0],
	        [0, 0, 0, 1],
	    ]       )





def 						__A						(      __lowerCamelCase				,     __lowerCamelCase = None       ) ->			np.ndarray:
	# Ensure event is not empty
	if event is None:
		a									=				np.array([ct, x, y, z]       )  # Symbolic four vector
	else:
		event[0] *= c  # x0 is ct (speed of light * time)

	return transformation_matrix(__lowerCamelCase       ) @ event


if __name__ == "__main__":
		import doctest

		doctest.testmod()

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

		print(F'\n{numerical_vector}')







import inspect
import warnings
from typing import Any, Dict, Optional, Union

from packaging import version





def 						__A						(      *__lowerCamelCase				,     __lowerCamelCase = None				,     __lowerCamelCase=True				,     __lowerCamelCase=2       ) ->			Dict:
	from .. import __version__

	a									=				take_from
	a									=				()
	if not isinstance(args[0]				,     __lowerCamelCase       ):
		a									=				(args,)

	for attribute, version_name, message in args:
		if version.parse(version.parse(__lowerCamelCase       ).base_version       ) >= version.parse(__lowerCamelCase       ):
			raise ValueError(
			    f'The deprecation tuple {(attribute, version_name, message)} should be removed since diffusers\''
			    f' version {__version__} is >= {version_name}'       )

		a									=				None
		if isinstance(__lowerCamelCase				,     __lowerCamelCase       ) and attribute in deprecated_kwargs:
			values += (deprecated_kwargs.pop(__lowerCamelCase       ),)
			a									=				f'The `{attribute}` argument is deprecated and will be removed in version {version_name}.'
		elif hasattr(__lowerCamelCase				,     __lowerCamelCase       ):
			values += (getattr(__lowerCamelCase				,     __lowerCamelCase       ),)
			a									=				f'The `{attribute}` attribute is deprecated and will be removed in version {version_name}.'
		elif deprecated_kwargs is None:
			a									=				f'`{attribute}` is deprecated and will be removed in version {version_name}.'

		if warning is not None:
			a									=				warning + """ """ if standard_warn else """"""
			warnings.warn(warning + message				,     __lowerCamelCase				,     stacklevel=__lowerCamelCase       )

	if isinstance(__lowerCamelCase				,     __lowerCamelCase       ) and len(__lowerCamelCase       ) > 0:
		a									=				inspect.getouterframes(inspect.currentframe()       )[1]
		a									=				call_frame.filename
		a									=				call_frame.lineno
		a									=				call_frame.function
		a							,					a									=				next(iter(deprecated_kwargs.items()       )       )
		raise TypeError(f'{function} in {filename} line {line_number-1} got an unexpected keyword argument `{key}`'       )

	if len(__lowerCamelCase       ) == 0:
		return
	elif len(__lowerCamelCase       ) == 1:
		return values[0]
	return values

