





"""simple docstring"""




from math import cos, sin





def 			a_							(				_lowercase  ):
						_UpperCamelCase     :   Any      =       float(_lowercase  )
						return [[scaling_factor * int(x == y  ) for x in range(2  )] for y in range(2  )]





def 			a_							(				_lowercase  ):
						_UpperCamelCase     :   str      =       cos(_lowercase  ), sin(_lowercase  )
						return [[c, -s], [s, c]]





def 			a_							(				_lowercase  ):
						_UpperCamelCase     :   List[Any]      =       cos(_lowercase  ), sin(_lowercase  )
						_UpperCamelCase     :   Optional[Any]      =       c * s
						return [[c * c, cs], [cs, s * s]]





def 			a_							(				_lowercase  ):
						_UpperCamelCase     :   Any      =       cos(_lowercase  ), sin(_lowercase  )
						_UpperCamelCase     :   List[Any]      =       c * s
						return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(F"    {scaling(5) = }")
print(F"  {rotation(45) = }")
print(F"{projection(45) = }")






print(F"{reflection(45) = }")









"""simple docstring"""





import inspect
import os
import unittest

import torch

import accelerate
from accelerate import debug_launcher
from accelerate.test_utils import (
    execute_subprocess_async,
    require_cpu,
    require_multi_gpu,
    require_single_gpu,
    test_sync,
)
from accelerate.utils import patch_environment

class    __lowercase							(      unittest.TestCase						):


				'''simple docstring'''


				def    _lowerCamelCase       ( self :  Any   ):
										snake_case__							:       Dict				      =       inspect.getfile(accelerate.test_utils   )
										snake_case__							:       Tuple				      =       os.path.sep.join(mod_file.split(os.path.sep   )[:-1] + ['''scripts''', '''test_sync.py''']   )

				@require_cpu
				def    _lowerCamelCase       ( self :  Optional[Any]   ):
										debug_launcher(test_sync.main   ,num_processes=1   )

				@require_cpu
				def    _lowerCamelCase       ( self :  List[str]   ):
										debug_launcher(test_sync.main   )

				@require_single_gpu
				def    _lowerCamelCase       ( self :  Union[str, Any]   ):
										test_sync.main()





				@require_multi_gpu
				def    _lowerCamelCase       ( self :  List[str]   ):
										print(F'''Found {torch.cuda.device_count()} devices.'''   )
										snake_case__							:       Dict				      =       ['''torchrun''', F'''--nproc_per_node={torch.cuda.device_count()}''', self.test_file_path]
										with patch_environment(omp_num_threads=1   ):
																execute_subprocess_async(SCREAMING_SNAKE_CASE_   ,env=os.environ.copy()   )


