code: 
  
  
  
  
  
  
  from __future__ import annotations
  
  def lowercase						(     SCREAMING_SNAKE_CASE					,						SCREAMING_SNAKE_CASE					,						SCREAMING_SNAKE_CASE					,						) ->       list[float | int]:
  
  
  			'''simple docstring'''
  
  
  
  
  
  
  
  			if not all((nth_term, start_term_a, common_ratio_r)   ):
  						return []
  			SCREAMING_SNAKE_CASE_			=	[]
  			SCREAMING_SNAKE_CASE_			=	1
  			SCREAMING_SNAKE_CASE_			=	common_ratio_r
  			for _ in range(int(SCREAMING_SNAKE_CASE   )   ):
  						if not series:
  									series.append(SCREAMING_SNAKE_CASE   )
  						else:
  									power += 1
  									series.append(float(start_term_a * multiple   )   )
  									SCREAMING_SNAKE_CASE_			=	pow(float(SCREAMING_SNAKE_CASE   )					,						SCREAMING_SNAKE_CASE   )
  			return series
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  				SCREAMING_SNAKE_CASE__    :    Dict								=					float(input("Enter the last number (n term) of the Geometric Series"))
  				SCREAMING_SNAKE_CASE__    :    List[Any]								=					float(input("Enter the starting term (a) of the Geometric Series"))
  				SCREAMING_SNAKE_CASE__    :    Any								=					float(
  				    input("Enter the common ratio between two terms (r) of the Geometric Series")
  				)
  				print("Formula of Geometric Series => a + ar + ar^2 ... +ar^n")
  				print(geometric_series(nth_term, start_term_a, common_ratio_r))
  
style_context: 
  
  
  
  
  import os
  import pickle
  import unittest
  from collections import UserDict, namedtuple
  
  import torch
  
  from accelerate.test_utils.testing import require_cuda, require_torch_min_version
  from accelerate.test_utils.training import RegressionModel
  from accelerate.utils import (
      convert_outputs_to_fpaa,
      extract_model_from_parallel,
      find_device,
      listify,
      patch_environment,
      recursively_apply,
      send_to_device,
  )
  
  
  SCREAMING_SNAKE_CASE__    :    Optional[Any]								=					namedtuple("ExampleNamedTuple", "a b c")
  
  
  
  class 			a_					(    unittest.TestCase    ):
  
  
  
  
  
  	def 	A_(       self			)     ->				List[str]:
  
  
  
  
  				"""simple docstring"""
  
  
  
  				SCREAMING_SNAKE_CASE_			=	torch.randn(5			,    2			)
  				SCREAMING_SNAKE_CASE_			=	torch.device('cuda'			) if torch.cuda.is_available() else torch.device('cpu'			)
  
  				SCREAMING_SNAKE_CASE_			=	send_to_device(SCREAMING_SNAKE_CASE			,    SCREAMING_SNAKE_CASE			)
  				self.assertTrue(torch.equal(resulta.cpu()			,    SCREAMING_SNAKE_CASE			)			)
  
  				SCREAMING_SNAKE_CASE_			=	send_to_device((tensor, [tensor, tensor], 1)			,    SCREAMING_SNAKE_CASE			)
  				self.assertIsInstance(SCREAMING_SNAKE_CASE			,    SCREAMING_SNAKE_CASE			)
  				self.assertTrue(torch.equal(resulta[0].cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertIsInstance(resulta[1]			,    SCREAMING_SNAKE_CASE			)
  				self.assertTrue(torch.equal(resulta[1][0].cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertTrue(torch.equal(resulta[1][1].cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertEqual(resulta[2]			,    1			)
  
  				SCREAMING_SNAKE_CASE_			=	send_to_device({'a': tensor, 'b': [tensor, tensor], 'c': 1}			,    SCREAMING_SNAKE_CASE			)
  				self.assertIsInstance(SCREAMING_SNAKE_CASE			,    SCREAMING_SNAKE_CASE			)
  				self.assertTrue(torch.equal(resulta['a'].cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertIsInstance(resulta['b']			,    SCREAMING_SNAKE_CASE			)
  				self.assertTrue(torch.equal(resulta['b'][0].cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertTrue(torch.equal(resulta['b'][1].cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertEqual(resulta['c']			,    1			)
  
  				SCREAMING_SNAKE_CASE_			=	send_to_device(ExampleNamedTuple(a=SCREAMING_SNAKE_CASE			,    b=[tensor, tensor]			,    c=1			)			,    SCREAMING_SNAKE_CASE			)
  				self.assertIsInstance(SCREAMING_SNAKE_CASE			,    SCREAMING_SNAKE_CASE			)
  				self.assertTrue(torch.equal(resulta.a.cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertIsInstance(resulta.b			,    SCREAMING_SNAKE_CASE			)
  				self.assertTrue(torch.equal(resulta.b[0].cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertTrue(torch.equal(resulta.b[1].cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertEqual(resulta.c			,    1			)
  
  				SCREAMING_SNAKE_CASE_			=	send_to_device(UserDict({'a': tensor, 'b': [tensor, tensor], 'c': 1}			)			,    SCREAMING_SNAKE_CASE			)
  				self.assertIsInstance(SCREAMING_SNAKE_CASE			,    SCREAMING_SNAKE_CASE			)
  				self.assertTrue(torch.equal(resulta['a'].cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertIsInstance(resulta['b']			,    SCREAMING_SNAKE_CASE			)
  				self.assertTrue(torch.equal(resulta['b'][0].cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertTrue(torch.equal(resulta['b'][1].cpu()			,    SCREAMING_SNAKE_CASE			)			)
  				self.assertEqual(resulta['c']			,    1			)
  
  
  
  
  
  	def 	A_(       self			)     ->				int:
  
  
  
  
  				"""simple docstring"""
  
  
  
  				with self.assertRaises(SCREAMING_SNAKE_CASE			) as cm:
  							SCREAMING_SNAKE_CASE_			=	recursively_apply(torch.tensor			,    (torch.tensor(1			), 1)			,    error_on_other_type=SCREAMING_SNAKE_CASE			)
  				self.assertEqual(
  				    str(cm.exception			)			,    'Unsupported types (<class \'int\'>) passed to `tensor`. Only nested list/tuple/dicts of objects that are valid for `is_torch_tensor` should be passed.'			,    )
  
  
  
  
  
  	def 	A_(       self			)     ->				int:
  
  
  
  
  				"""simple docstring"""
  
  
  
  				SCREAMING_SNAKE_CASE_			=	torch.tensor([1, 2, 3, 4, 5]			)
  				self.assertEqual(listify(SCREAMING_SNAKE_CASE			)			,    [1, 2, 3, 4, 5]			)
  
  				SCREAMING_SNAKE_CASE_			=	torch.tensor([[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]]			)
  				self.assertEqual(listify(SCREAMING_SNAKE_CASE			)			,    [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]]			)
  
  				SCREAMING_SNAKE_CASE_			=	torch.tensor([[[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]], [[11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]]			)
  				self.assertEqual(
  				    listify(SCREAMING_SNAKE_CASE			)			,    [[[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]], [[11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]]			)
  
  
  
  
  
  	def 	A_(       self			)     ->				Tuple:
  
  
  
  
  				"""simple docstring"""
  
  
  
  				with patch_environment(aa=1			,    BB=2			):
  							self.assertEqual(os.environ.get('AA'			)			,    '1'			)
  							self.assertEqual(os.environ.get('BB'			)			,    '2'			)
  
  				self.assertNotIn('AA'			,    os.environ			)
  				self.assertNotIn('BB'			,    os.environ			)
  
  
  
  
  
  	def 	A_(       self			)     ->				Dict:
  
  
  
  
  				"""simple docstring"""
  
  
  
  				SCREAMING_SNAKE_CASE_			=	RegressionModel()
  				SCREAMING_SNAKE_CASE_			=	model.forward
  				SCREAMING_SNAKE_CASE_			=	convert_outputs_to_fpaa(model.forward			)
  				SCREAMING_SNAKE_CASE_			=	extract_model_from_parallel(SCREAMING_SNAKE_CASE			,    keep_fpaa_wrapper=SCREAMING_SNAKE_CASE			)
  				SCREAMING_SNAKE_CASE_			=	pickle.dumps(SCREAMING_SNAKE_CASE			)
  
  
  
  
  
  	@require_cuda
  	def 	A_(       self			)     ->				int:
  
  
  
  
  				"""simple docstring"""
  
  
  
  				SCREAMING_SNAKE_CASE_			=	RegressionModel()
  				SCREAMING_SNAKE_CASE_			=	model.forward
  				SCREAMING_SNAKE_CASE_			=	torch.cuda.amp.autocast(dtype=torch.floataa			)(model.forward			)
  				SCREAMING_SNAKE_CASE_			=	convert_outputs_to_fpaa(model.forward			)
  				SCREAMING_SNAKE_CASE_			=	extract_model_from_parallel(SCREAMING_SNAKE_CASE			,    keep_fpaa_wrapper=SCREAMING_SNAKE_CASE			)
  				SCREAMING_SNAKE_CASE_			=	pickle.dumps(SCREAMING_SNAKE_CASE			)
  
  
  
  
  
  	@require_cuda
  	@require_torch_min_version(version='2.0'			)
  	def 	A_(       self			)     ->				Optional[Any]:
  
  
  
  
  				"""simple docstring"""
  
  
  
  				SCREAMING_SNAKE_CASE_			=	RegressionModel()
  				SCREAMING_SNAKE_CASE_			=	model.forward
  				SCREAMING_SNAKE_CASE_			=	torch.cuda.amp.autocast(dtype=torch.floataa			)(model.forward			)
  				SCREAMING_SNAKE_CASE_			=	convert_outputs_to_fpaa(model.forward			)
  				SCREAMING_SNAKE_CASE_			=	torch.compile(model.forward			,    backend='inductor'			)
  				SCREAMING_SNAKE_CASE_			=	torch.randn(4			,    10			).cuda()
  				SCREAMING_SNAKE_CASE_			=	model(SCREAMING_SNAKE_CASE			)
  
  
  
  
  
  	def 	A_(       self			)     ->				List[str]:
  
  
  
  
  				"""simple docstring"""
  
  
  
  				SCREAMING_SNAKE_CASE_			=	RegressionModel()
  				# could also do a test with DistributedDataParallel, but difficult to run on CPU or single GPU
  				SCREAMING_SNAKE_CASE_			=	torch.nn.parallel.DataParallel(SCREAMING_SNAKE_CASE			)
  				SCREAMING_SNAKE_CASE_			=	extract_model_from_parallel(SCREAMING_SNAKE_CASE			)
  
  				self.assertEqual(SCREAMING_SNAKE_CASE			,    SCREAMING_SNAKE_CASE			)
  
  
  
  
  
  	@require_torch_min_version(version='2.0'			)
  	def 	A_(       self			)     ->				int:
  
  
  
  
  				"""simple docstring"""
  
  
  
  				SCREAMING_SNAKE_CASE_			=	RegressionModel()
  				SCREAMING_SNAKE_CASE_			=	torch.compile(SCREAMING_SNAKE_CASE			)
  
  				# could also do a test with DistributedDataParallel, but difficult to run on CPU or single GPU
  				SCREAMING_SNAKE_CASE_			=	torch.nn.parallel.DataParallel(SCREAMING_SNAKE_CASE			)
  				SCREAMING_SNAKE_CASE_			=	torch.compile(SCREAMING_SNAKE_CASE			)
  				SCREAMING_SNAKE_CASE_			=	extract_model_from_parallel(SCREAMING_SNAKE_CASE			)
  
  				self.assertEqual(compiled_model._orig_mod			,    compiled_model_unwrapped._orig_mod			)
  
  
  
  
  
  	def 	A_(       self			)     ->				Optional[Any]:
  
  
  
  
  				"""simple docstring"""
  
  
  
  				self.assertEqual(find_device([1, 'a', torch.tensor([1, 2, 3]			)]			)			,    torch.device('cpu'			)			)
  				self.assertEqual(find_device({'a': 1, 'b': torch.tensor([1, 2, 3]			)}			)			,    torch.device('cpu'			)			)
  				self.assertIsNone(find_device([1, 'a']			)			)
  